{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-26T00:14:02.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61310,"title":"Electric Power Steering (EPS) Assist Curve Calculation","description":"Electric Power Steering (EPS) provides assist torque proportional to driver input.\r\nGiven Steering torque Ts and Gain k, Compute assist torque Ta.\r\nEquation:\r\nTa = k × Ts","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eElectric Power Steering (EPS) provides assist torque proportional to driver input.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Steering torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTs \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGain \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute assist torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTa\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTa = k × Ts\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Ta = epsAssist(Ts,k)\r\nTa =0;\r\nend","test_suite":"%%\r\nTs = 4; \r\nk = 3;\r\nTa_expected = 12;\r\nassert(isequal(epsAssist(Ts,k),Ta_expected))\r\n\r\n%%\r\nTs = 5; \r\nk = 2;\r\nTa_expected = 10;\r\nassert(isequal(epsAssist(Ts,k),Ta_expected))\r\n\r\n%%\r\nTs = 6; \r\nk = 1.5;\r\nTa_expected = 9;\r\nassert(isequal(epsAssist(Ts,k),Ta_expected))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:39:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:39:20.000Z","updated_at":"2026-04-29T17:30:10.000Z","published_at":"2026-04-28T09:39:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eElectric Power Steering (EPS) provides assist torque proportional to driver input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Steering torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTs \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eGain \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute assist torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTa\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTa = k × Ts\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61307,"title":"Steering Ratio Calculation","description":"The steering ratio defines the relationship between steering wheel angle and road wheel angle.\r\nGiven wheel angle δ and Steering ratio N, Compute steering wheel angle swa.\r\nEquation:\r\nswa = N × delta","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe steering ratio defines the relationship between steering wheel angle and road wheel angle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand Steering ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eN, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute steering wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eswa\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eswa = N × delta\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function sw = steeringWheelAngle(delta,N)\r\nsw = N;\r\nend","test_suite":"%%\r\ndelta = 5*pi/180; \r\nN = 16;\r\nsw_expected = 1.3963;\r\nassert(abs(steeringWheelAngle(delta,N) - sw_expected) \u003c 1e-4)\r\n\r\n%%\r\ndelta = 3*pi/180; \r\nN = 18;\r\nsw_expected = 0.9425;\r\nassert(abs(steeringWheelAngle(delta,N) - sw_expected) \u003c 1e-4)\r\n\r\n%%\r\ndelta = 10*pi/180; \r\nN = 14;\r\nsw_expected = 2.4435;\r\nassert(abs(steeringWheelAngle(delta,N) - sw_expected) \u003c 1e-4)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:26:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:26:22.000Z","updated_at":"2026-04-29T17:24:14.000Z","published_at":"2026-04-28T09:26:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe steering ratio defines the relationship between steering wheel angle and road wheel angle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand Steering ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute steering wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswa\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eswa = N × delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61309,"title":"Steering Torque Estimation","description":"Steering torque is generated due to lateral tire forces acting through the steering mechanism.\r\nGiven Lateral force Fy and Lever arm r, Compute torque T.\r\nEquation:\r\nT = Fy × r","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteering torque is generated due to lateral tire forces acting through the steering mechanism.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Lateral force \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFy \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLever arm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eT = Fy × r\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = steeringTorque(Fy,r)\r\nT = 0;\r\nend","test_suite":"%%\r\nFy = 1500; \r\nr = 0.15;\r\nT_expected = 225;\r\nassert(isequal(steeringTorque(Fy,r),T_expected))\r\n\r\n%%\r\nFy = 1000; \r\nr = 0.2;\r\nT_expected = 200;\r\nassert(isequal(steeringTorque(Fy,r),T_expected))\r\n\r\n%%\r\nFy = 800; \r\nr = 0.25;\r\nT_expected = 200;\r\nassert(isequal(steeringTorque(Fy,r),T_expected))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:36:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:36:45.000Z","updated_at":"2026-04-30T06:50:23.000Z","published_at":"2026-04-28T09:36:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSteering torque is generated due to lateral tire forces acting through the steering mechanism.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Lateral force \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFy \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eLever arm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = Fy × r\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61308,"title":"Understeer or Oversteer Gradient Calculation","description":"This gradient determines whether a vehicle tends to understeer or oversteer.\r\nGiven Mass m, Wheelbase L, Front cornering stiffness Cf and Rear cornering stiffness Cr, Compute understeer/oversteer gradient K.\r\nEquation:\r\nK = (m / L) × ( (1 / Cf) − (1 / Cr) )","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis gradient determines whether a vehicle tends to understeer or oversteer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003em, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFront cornering stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRear cornering stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCr, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute understeer/oversteer gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eK\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eK = (m / L) × ( (1 / Cf) − (1 / Cr) )\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function K = understeerGradient(m,L,Cf,Cr)\r\nK = Cr;\r\nend","test_suite":"%%\r\nm = 1500; \r\nL = 2.7; \r\nCf = 80000; \r\nCr = 90000;\r\nK_expected = 0.001543;\r\nassert(abs(understeerGradient(m,L,Cf,Cr) - K_expected) \u003c 1e-3)\r\n\r\n%%\r\nm = 1200; \r\nL = 2.5; \r\nCf = 70000; \r\nCr = 85000;\r\nK_expected = 0.001029;\r\nassert(abs(understeerGradient(m,L,Cf,Cr) - K_expected) \u003c 1e-3)\r\n\r\n%%\r\nm = 1800; \r\nL = 3.0; \r\nCf = 90000; \r\nCr = 95000;\r\nK_expected = 0.000351;\r\nassert(abs(understeerGradient(m,L,Cf,Cr) - K_expected) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:34:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:31:51.000Z","updated_at":"2026-04-30T16:28:44.000Z","published_at":"2026-04-28T09:34:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis gradient determines whether a vehicle tends to understeer or oversteer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eWheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFront cornering stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eRear cornering stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCr, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute understeer/oversteer gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = (m / L) × ( (1 / Cf) − (1 / Cr) )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61304,"title":"Turning radius of a vehicle","description":"The turning radius represents the radius of the circular path followed by a vehicle.\r\nGiven Wheelbase L and Steering angle δ, Compute the turning radius R.\r\nEquation:\r\nR = L / tan(delta)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Wheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteering angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδ, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the turning radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eR = L / tan(delta)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function R = turningRadius(L,delta)\r\nR = 0;\r\nend","test_suite":"%%\r\nL = 2.5; delta = 30*pi/180;\r\nR_expected = 4.3301;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 3.0; delta = 20*pi/180;\r\nR_expected = 8.2426;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 2.8; delta = 10*pi/180;\r\nR_expected = 15.866;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-1)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:16:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:13:54.000Z","updated_at":"2026-04-30T16:29:38.000Z","published_at":"2026-04-28T09:16:45.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Wheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSteering angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδ, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the turning radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = L / tan(delta)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61305,"title":"Yaw rate of the vehicle","description":"Yaw rate defines how quickly a vehicle rotates about its vertical axis during motion.\r\nGiven Vehicle speed v and Turning radius R, compute yaw rate r.\r\nEquation:\r\nr = v / R","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYaw rate defines how quickly a vehicle rotates about its vertical axis during motion.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Vehicle speed \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ev \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTurning radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eR, c\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eompute yaw rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er = v / R\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = yawRate(v,R)\r\nr = v;\r\nend","test_suite":"%%\r\nv = 15; R = 30;\r\nr_expected = 0.5;\r\nassert(abs(yawRate(v,R) - r_expected) \u003c 1e-6)\r\n\r\n%%\r\nv = 20; R = 40;\r\nr_expected = 0.5;\r\nassert(abs(yawRate(v,R) - r_expected) \u003c 1e-6)\r\n\r\n%%\r\nv = 10; R = 25;\r\nr_expected = 0.4;\r\nassert(abs(yawRate(v,R) - r_expected) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:18:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:18:24.000Z","updated_at":"2026-05-01T02:44:50.000Z","published_at":"2026-04-28T09:18:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYaw rate defines how quickly a vehicle rotates about its vertical axis during motion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Vehicle speed \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eTurning radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR, c\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eompute yaw rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er = v / R\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58743,"title":"Find the surface area of a cone.","description":"For instance,\r\nGiven r (radius) = 3, and s (slant height) = 5:\r\nsurface area should be 94.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 40.5px; transform-origin: 407.5px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor instance,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven r (radius) = 3, and s (slant height) = 5:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esurface area should be 94.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = findArea(r,s)\r\n  y = x;\r\nend","test_suite":"%%\r\nr = 3;\r\ns = 5;\r\ny_correct = 75;\r\nassert(isequal(findArea(r,s),y_correct))\r\n\r\n%%\r\nr = 1;\r\ns = 4;\r\ny_correct = 16;\r\nassert(isequal(findArea(r,s),y_correct))\r\n\r\n%%\r\nr = 2;\r\ns = 8;\r\ny_correct = 63;\r\nassert(isequal(findArea(r,s),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3470333,"edited_by":3470333,"edited_at":"2023-07-18T20:23:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2023-07-18T20:23:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-18T20:21:34.000Z","updated_at":"2026-04-29T19:33:29.000Z","published_at":"2023-07-18T20:23:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor instance,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven r (radius) = 3, and s (slant height) = 5:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esurface area should be 94.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48015,"title":"Calculate the volume of the football","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63.9631px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 31.9744px; transform-origin: 406.996px 31.9815px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9091px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4545px; text-align: left; transform-origin: 383.999px 10.4545px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate the volume of a football given the ball radius r, using the formula below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.0625px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 17.0312px; text-align: left; transform-origin: 383.999px 17.0312px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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width=\"88\" height=\"34\" style=\"width: 88px; height: 34px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = calcVolume(r)\r\n\r\n    y = r;\r\nend","test_suite":"%%\r\nr = 2;\r\ny_correct = 33.5103;\r\nassert(abs(calcVolume(r) - y_correct) \u003c 0.1)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":808745,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T14:17:48.000Z","updated_at":"2026-04-05T10:34:30.000Z","published_at":"2020-12-17T14:17:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the volume of a football given the ball radius r, using the formula below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV_{sphere} = \\\\frac43 \\\\pi r^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44880,"title":"Angle between two vectors","description":"Given 2 pairs of _cartesian co-ordinates_, determine the angle between the 2 vectors formed by the _points_ and the _origin_. Angle must be in [0,180] and in degrees.\r\n\r\ne.g. \r\n\r\n* Input (3 separate inputs)\r\n\r\n  [0 1;2 0]\r\n  [1 1;-2 0]\r\n  [1 1;2 2]\r\n\r\n* Output (3 separate outputs):\r\n\r\n  90\r\n  135\r\n  0","description_html":"\u003cp\u003eGiven 2 pairs of \u003ci\u003ecartesian co-ordinates\u003c/i\u003e, determine the angle between the 2 vectors formed by the \u003ci\u003epoints\u003c/i\u003e and the \u003ci\u003eorigin\u003c/i\u003e. Angle must be in [0,180] and in degrees.\u003c/p\u003e\u003cp\u003ee.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003eInput (3 separate inputs)\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e[0 1;2 0]\r\n[1 1;-2 0]\r\n[1 1;2 2]\r\n\u003c/pre\u003e\u003cul\u003e\u003cli\u003eOutput (3 separate outputs):\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e90\r\n135\r\n0\r\n\u003c/pre\u003e","function_template":"function y = angle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 1;-1 -1];\r\ny_correct = 180;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;-1 -1];\r\ny_correct = 90;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0.5 sqrt(3)/2;0.2 0];\r\ny_correct = 60;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;0.5 sqrt(3)/2];\r\ny_correct = 75;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0 1;0 5];\r\ny_correct = 0;\r\nassert(isequal(angle(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":290843,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-02T11:16:36.000Z","updated_at":"2026-02-28T08:22:03.000Z","published_at":"2019-04-02T11:17:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven 2 pairs of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecartesian co-ordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, determine the angle between the 2 vectors formed by the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epoints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eorigin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Angle must be in [0,180] and in degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput (3 separate inputs)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[0 1;2 0]\\n[1 1;-2 0]\\n[1 1;2 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput (3 separate outputs):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[90\\n135\\n0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42686,"title":"What's the missing interior angle?","description":"I'm talking about polygons...  The sum of the interior angles of a triangle is 180 degrees.  The sum of the interior angles of a quadrilateral is 360 degrees, and so on.\r\n\r\nFor this problem, you are given n-1 angles (in degrees) of an n-sided polygon.  Please return the final angle.\r\n\r\nTriangle examples:\r\n\r\n  \u003e\u003ea=missing_interior_angle([60 60])\r\n  a =\r\n      60\r\n  \u003e\u003ea=missing_interior_angle([45 45])\r\n  a =\r\n      90","description_html":"\u003cp\u003eI'm talking about polygons...  The sum of the interior angles of a triangle is 180 degrees.  The sum of the interior angles of a quadrilateral is 360 degrees, and so on.\u003c/p\u003e\u003cp\u003eFor this problem, you are given n-1 angles (in degrees) of an n-sided polygon.  Please return the final angle.\u003c/p\u003e\u003cp\u003eTriangle examples:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt;a=missing_interior_angle([60 60])\r\na =\r\n    60\r\n\u0026gt;\u0026gt;a=missing_interior_angle([45 45])\r\na =\r\n    90\r\n\u003c/pre\u003e","function_template":"function y = missing_interior_angle(x)\r\n  y = 180 - sum(x);\r\nend","test_suite":"%%\r\nx = [60 60];\r\ny_correct = 60;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = [45 90];\r\ny_correct = 45;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = [90 70 70];\r\ny_correct = 130;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = [120 120 120 110 110];\r\ny_correct = 140;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = 140*ones(1,8);\r\ny_correct = 140;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":57863,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":92,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-11-16T01:39:37.000Z","updated_at":"2026-02-10T11:40:46.000Z","published_at":"2015-11-16T01:40:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI'm talking about polygons... The sum of the interior angles of a triangle is 180 degrees. The sum of the interior angles of a quadrilateral is 360 degrees, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you are given n-1 angles (in degrees) of an n-sided polygon. Please return the final angle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangle examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003ea=missing_interior_angle([60 60])\\na =\\n    60\\n\u003e\u003ea=missing_interior_angle([45 45])\\na =\\n    90]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46063,"title":"Area of a pentagon","description":"Given the side of a regular pentagon and its apothem return the area of pentagon.\r\n\r\nRemember the area of pentagon is calculate as the product between perimeter and the apothem divided by 2. ","description_html":"\u003cp\u003eGiven the side of a regular pentagon and its apothem return the area of pentagon.\u003c/p\u003e\u003cp\u003eRemember the area of pentagon is calculate as the product between perimeter and the apothem divided by 2.\u003c/p\u003e","function_template":"function area = pentagon_Area(s,A)\r\n  area=s^2;\r\nend","test_suite":"%%\r\ns = 8;\r\nA = 9;\r\narea_correct = 180;\r\nassert(isequal(pentagon_Area(s,A),area_correct))\r\n\r\n%%\r\ns=pi;\r\nA=9;\r\narea_correct=(45/2)*pi;\r\nassert(isequal(pentagon_Area(s,A),area_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":426918,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":85,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-27T22:20:36.000Z","updated_at":"2026-04-13T13:29:19.000Z","published_at":"2020-07-27T22:21:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the side of a regular pentagon and its apothem return the area of pentagon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemember the area of pentagon is calculate as the product between perimeter and the apothem divided by 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45468,"title":"Determine the perimeter of a three-quarter circle","description":"If a circle has a diameter of x as an input value, then show the value of the perimeter of the three-quarter circle in output variable y. Remember that, you must show the output value of the perimeter, y to 15 decimal place.  \r\n","description_html":"\u003cp\u003eIf a circle has a diameter of x as an input value, then show the value of the perimeter of the three-quarter circle in output variable y. Remember that, you must show the output value of the perimeter, y to 15 decimal place.\u003c/p\u003e","function_template":"function y = circle_diameter(x)\r\ny = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 6.712388980384690;\r\nassert(isequal(circle_diameter(x),y_correct))\r\n\r\n%%\r\nx = 5.5;\r\ny_correct = 18.459069696057895;\r\nassert(isequal(circle_diameter(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":430818,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":"2020-04-26T21:34:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-19T16:22:42.000Z","updated_at":"2026-02-16T12:04:56.000Z","published_at":"2020-04-19T17:29:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a circle has a diameter of x as an input value, then show the value of the perimeter of the three-quarter circle in output variable y. Remember that, you must show the output value of the perimeter, y to 15 decimal place.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45488,"title":"Height of a 3D Pyramid ","description":"If a pyramid is made with one(1). What will be the height of the pyramid of square shaped base(n*n)? where input is n.","description_html":"\u003cp\u003eIf a pyramid is made with one(1). What will be the height of the pyramid of square shaped base(n*n)? where input is n.\u003c/p\u003e","function_template":"function h = pyramid(n)\r\n  h = n;\r\nend","test_suite":"%%\r\nn = 10;\r\ny_correct = 5;\r\nassert(isequal(pyramid(n),y_correct))\r\n%%\r\nn = 19;\r\ny_correct = 10;\r\nassert(isequal(pyramid(n),y_correct))\r\n%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(pyramid(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":432893,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2020-04-30T19:41:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-30T19:37:13.000Z","updated_at":"2026-02-11T12:11:39.000Z","published_at":"2020-04-30T19:37:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a pyramid is made with one(1). What will be the height of the pyramid of square shaped base(n*n)? where input is n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45333,"title":"Area-01","description":"Given the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\r\n\r\n","description_html":"\u003cp\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/p\u003e","function_template":"function y = inscribed_circle(r)\r\n  y = x;\r\nend","test_suite":"%%\r\nr = 1;\r\ny_correct = 0.8584;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 5;\r\ny_correct = 21.4602;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 0;\r\ny_correct = 0;\r\nassert(isequal(inscribed_circle(r),y_correct))\r\n%%\r\nr = 12.1;\r\ny_correct = 125.6794;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-16T18:24:27.000Z","updated_at":"2026-02-09T14:23:49.000Z","published_at":"2020-02-16T18:24:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2999,"title":"Billiards","description":"Considering there are 15 pool balls, (b), in the game of pool, and given a radius, (r). What is the volume, (V), of a rack in the game of pool?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381px 8px; transform-origin: 381px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsidering there are 15 pool balls, (b), in the game of pool, and given a radius, (r). What is the volume, (V), of a rack in the game of pool?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Volume_Rack(x)\r\nend","test_suite":"\r\n%%\r\nx = 2.438;\r\ny_correct = 910.502;\r\ny_calc = Volume_Rack(x);\r\nassert(abs((y_correct - y_calc) / y_correct) \u003c 1e-4)\r\n\r\n%%\r\nx = 2.25;\r\ny_correct = 715.694;\r\ny_calc = Volume_Rack(x);\r\nassert(abs((y_correct - y_calc) / y_correct) \u003c 1e-4)\r\n\r\n%%\r\nx = 2;\r\ny_correct = 502.659;\r\ny_calc = Volume_Rack(x);\r\nassert(abs((y_correct - y_calc) / y_correct) \u003c 1e-4)","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":34016,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2021-11-02T04:54:44.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-02-11T01:06:55.000Z","updated_at":"2026-02-17T09:08:22.000Z","published_at":"2015-02-11T01:30:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsidering there are 15 pool balls, (b), in the game of pool, and given a radius, (r). What is the volume, (V), of a rack in the game of pool?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44240,"title":"Area of a Square","description":"Given the length x of the side of a regular square, find the area of the square, A.","description_html":"\u003cp\u003eGiven the length x of the side of a regular square, find the area of the square, A.\u003c/p\u003e","function_template":"function A = sq_area(x)\r\n  A = x;\r\nend","test_suite":"%%\r\nx = 1;\r\nA = 1;\r\nassert(isequal(sq_area(x),A))\r\n\r\n%%\r\nx = 2;\r\nA = 4;\r\nassert(isequal(sq_area(x),A))\r\n\r\n%%\r\nx = 6;\r\nA = 36;\r\nassert(isequal(sq_area(x),A))\r\n\r\n%%\r\nx = 8;\r\nA = 64;\r\nassert(isequal(sq_area(x),A))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":138544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":733,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-06-20T20:38:32.000Z","updated_at":"2026-04-23T00:00:49.000Z","published_at":"2017-06-21T15:37:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the length x of the side of a regular square, find the area of the square, A.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45217,"title":"Find a common vertex","description":"First input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4]\r\nand\r\ni = 2\r\nthe output is the vector\r\nrow_idx = [1 3 4]\r\nsince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 479.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 239.8px; transform-origin: 408px 239.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.725px 8px; transform-origin: 375.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 3;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e     1 3 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e     1 4 2;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2 3 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 3 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.533px 8px; transform-origin: 367.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_vertex(T,i)\r\n  row_idx = i;\r\nend","test_suite":"%% Tetrahedron\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4];\r\n\r\ni = 2;\r\n\r\nrow_idx = [1 3 4];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 5;...\r\n     1 5 2;...\r\n     6 3 2;...\r\n     6 4 3;...\r\n     6 5 4;...\r\n     6 2 5];\r\n\r\ni = 4;\r\n\r\nrow_idx = [2 3 6 7];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n     2 3 4;...\r\n     5 6 8;...\r\n     6 7 8;...\r\n     1 2 5;...\r\n     2 5 6;...\r\n     2 3 6;...\r\n     3 6 7;...\r\n     3 4 7;...\r\n     4 7 8;...\r\n     4 1 8;...\r\n     1 8 5];\r\n\r\ni = 6;\r\n\r\nrow_idx = [3 4 6 7 8];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n     3 5 7;...\r\n     5 7 11;...\r\n     7 11 13];\r\n\r\ni = 8;\r\n\r\nassert(isempty(find_common_vertex(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_vertex.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2025-07-09T05:47:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T16:22:33.000Z","updated_at":"2026-04-17T18:43:23.000Z","published_at":"2019-12-01T16:58:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if inputs are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [1 2 3;...\\n     1 3 4;...\\n     1 4 2;...\\n     2 3 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[i = 2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe output is the vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[row_idx = [1 3 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2465,"title":"Find the area of a rectangle if length of the diagonal is given.","description":"if length of a diagnonal in rectangle is 5. Its area is 12.","description_html":"\u003cp\u003eif length of a diagnonal in rectangle is 5. Its area is 12.\u003c/p\u003e","function_template":"function y = area_rect(x)\r\n  y = ;\r\nend","test_suite":"%%\r\nx=5;\r\ny_correct = 12;\r\nassert(isequal(area_rect(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":28146,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":169,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-25T13:24:47.000Z","updated_at":"2026-02-18T10:51:56.000Z","published_at":"2014-07-25T13:26:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif length of a diagnonal in rectangle is 5. Its area is 12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60576,"title":"Perimeter of a Koch snowflake","description":"A Koch snowflake is an iteratively generated (fractal) shape built out of successively smaller equilateral triangles by following these steps: \r\nDraw an equilateral triangle. (n = 0)\r\nDivide the line segment into three segments of equal length.\r\nDraw an equilateral triangle that has the middle segment from step 2 as its base and points outward.\r\nremove the line segment that is the base of the triangle from step 3. (n = 1) \r\nRepeat steps 2 - 4. (n = 2,3,...) \r\nIn the limit of  this shape has an infinite perimeter and a finite area. For , this perimeter is calculable. Calculate both of these values for any input value of n and any starting triangle edge length, s.\r\n[A1,P1] = KochSnowflake(n,s)\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 554.062px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 277.025px; transform-origin: 332px 277.031px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 21px; text-align: left; transform-origin: 309px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Koch snowflake is an iteratively generated (fractal) shape built out of successively smaller equilateral triangles by following these steps: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 122.625px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 316px 61.3125px; transform-origin: 316px 61.3125px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDraw an equilateral triangle. (n = 0)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDivide the line segment into three segments of equal length.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 20.4375px; text-align: left; transform-origin: 288px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDraw an equilateral triangle that has the middle segment from step 2 as its base and points outward.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eremove the line segment that is the base of the triangle from step 3. (n = 1) \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRepeat steps 2 - 4. (n = 2,3,...) \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the limit of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e this shape has an infinite perimeter and a finite area. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43\" height=\"18\" style=\"width: 43px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, this perimeter is calculable. Calculate both of these values for any input value of n and any starting triangle edge length, s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 329px 10.2125px; transform-origin: 329px 10.2188px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[A1,P1] = KochSnowflake(n,s)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 256px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 309px 128px; text-align: left; transform-origin: 309px 128px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"256\" height=\"256\" style=\"vertical-align: middle;width: 256px;height: 256px\" 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\" alt=\"n = 0,1,2,3 of Koch Snowflake\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Area,Perimeter] = KochSnowflake(n,s)\r\n  Area = [];\r\n  Perimeter =[];\r\nend","test_suite":"filetext = fileread('KochSnowflake.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'eval') || ...\r\n          contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\nassert(~illegal)\r\n%% \r\nn=1;s=sqrt(5);\r\nA_correct=5.773502691896258/2;\r\nP_correct=8.944271909999159;\r\n[A,P]=KochSnowflake(n,s);\r\n[A,A_correct]\r\nassert(all(abs([A,P]-[A_correct,P_correct])\u003c1E-12));\r\n%% \r\nn=2;s=sqrt(7);\r\nA_correct=8.981004187394181/2;\r\nP_correct=14.110673659011150;\r\n[A,P]=KochSnowflake(n,s);\r\n[A,A_correct]\r\nassert(all(abs([A,P]-[A_correct,P_correct])\u003c1E-12));\r\n%% \r\nn=20;s=sqrt(9);\r\nA_correct=12.470765391560523/2;\r\nP_correct=2838.031696810952;\r\n[A,P]=KochSnowflake(n,s);\r\n[A,A_correct]\r\nassert(all(abs([A,P]-[A_correct,P_correct])\u003c1E-12));\r\n%%\r\nn = 0;s=1:20;\r\nP_correct = 3*s;\r\nA_correct = s.^2*sqrt(3)/4;\r\nfor i = 1:20\r\n    [A,P]=KochSnowflake(n,s(i));\r\n    assert(all(abs([A,P]-[A_correct(i),P_correct(i)])\u003c1E-12));\r\nend\r\n%%\r\nn=1:20;s=1.5;\r\nP_correct = (9*(4/3).^n)/2;\r\nA_correct = 9*sqrt(3)*(8-3*(4/9).^n)/80;\r\nfor i = 1:20\r\n    [A,P]=KochSnowflake(n(i),s);\r\n    assert(all(abs([A,P]-[A_correct(i),P_correct(i)])\u003c1E-12));\r\nend\r\n%% \r\nn = 12345678900000000000;s=987654321000;\r\nP_correct = Inf;\r\nA_correct = 1.35163849E24/2;\r\n[A,P]=KochSnowflake(n,s);\r\nassert(abs(A-A_correct)\u003c1E15\u0026isinf(P));","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":4545451,"edited_by":4545451,"edited_at":"2024-07-03T20:47:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-07-03T20:47:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-07-03T19:30:17.000Z","updated_at":"2026-03-18T07:01:29.000Z","published_at":"2024-07-03T20:26:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Koch snowflake is an iteratively generated (fractal) shape built out of successively smaller equilateral triangles by following these steps: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDraw an equilateral triangle. (n = 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide the line segment into three segments of equal length.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDraw an equilateral triangle that has the middle segment from step 2 as its base and points outward.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eremove the line segment that is the base of the triangle from step 3. (n = 1) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat steps 2 - 4. (n = 2,3,...) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the limit of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\rightarrow \\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e this shape has an infinite perimeter and a finite area. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026lt; \\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, this perimeter is calculable. Calculate both of these values for any input value of n and any starting triangle edge length, s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[A1,P1] = KochSnowflake(n,s)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"256\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"256\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"n = 0,1,2,3 of Koch Snowflake\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59856,"title":"Calculate the Area of the Ring","description":"\r\nYou have Ring which consist of inner and outer Circles with Radius r and R which are not given but you'll be given Hprizontal distance d which is Tangent to inner circle .\r\nCalculate the Area of the Ring","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 312.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 156.017px; transform-origin: 406.5px 156.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 231.033px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 115.517px; text-align: left; transform-origin: 383.5px 115.517px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"225\" height=\"225\" style=\"vertical-align: baseline;width: 225px;height: 225px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.067px 7.81667px; transform-origin: 192.067px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have Ring which consist of inner and outer Circles with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.742px 7.81667px; transform-origin: 126.742px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRadius r and R which are not given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.1833px 7.81667px; transform-origin: 59.1833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.81667px; transform-origin: 96.5917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the Area of the Ring\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(d)\r\n  area = d;\r\nend","test_suite":"%%\r\nd = 3;\r\narea_correct = 28.2743;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 5;\r\narea_correct = 78.5398;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 8;\r\narea_correct = 201.0619;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 15;\r\narea_correct = 706.8583;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 17;\r\narea_correct = 907.9203;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4033021,"edited_by":223089,"edited_at":"2024-06-12T15:22:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2024-06-12T15:22:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-07T14:03:59.000Z","updated_at":"2026-04-18T06:50:15.000Z","published_at":"2024-04-07T14:20:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have Ring which consist of inner and outer Circles with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRadius r and R which are not given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the Area of the 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the shortest distance between a point and a straight line.","description":"Given the Cartesian coordinates of three points A, B and C (in a flat Euclidean space),\r\nfind the shortest distance between the straight line through A and B, and the point C.\r\n\r\nAssumption:\r\n\r\nA and B do not coincide.","description_html":"\u003cp\u003eGiven the Cartesian coordinates of three points A, B and C (in a flat Euclidean space),\r\nfind the shortest distance between the straight line through A and B, and the point C.\u003c/p\u003e\u003cp\u003eAssumption:\u003c/p\u003e\u003cp\u003eA and B do not coincide.\u003c/p\u003e","function_template":"function y = shortest_distance(x1,x2,x3)\r\n  y = 0;\r\nend","test_suite":"%%\r\nx1 = [0 0 0];\r\nx2 = [1 1 1];\r\nx3 = [2 2 2];\r\n\r\ny_correct = 0; \r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\nx1 = [0 0 0];\r\nx2 = [0 0 1];\r\nx3 = [1 0 0];\r\n\r\ny_correct = 1;\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\nx1 = [1 0 0];\r\nx2 = [0 1 0];\r\nx3 = [0 0 0];\r\n\r\ny_correct = sqrt(1/2);\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\ntheta = 0.5;\r\npsi = -0.2;\r\nphi = 1.1;\r\nR3=[cos(psi) sin(psi) 0.0; -sin(psi) cos(psi) 0.0; 0.0 0.0 1.0];\r\nR2=[cos(theta) 0.0 -sin(theta); 0.0 1.0 0.0; sin(theta) 0.0 cos(theta)];\r\nR1=[1.0 0.0 0.0; 0.0 cos(phi) sin(phi); 0.0 -sin(phi) cos(phi)];\r\n\r\nR = R3*R2*R1;\r\nx1 = [1 0 0]*R;\r\nx2 = [0 1 0]*R;\r\nx3 = [0 0 0]*R;\r\n\r\ny_correct = sqrt(1/2);\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\nx1 = [0 0 0];\r\nx2 = [0 0 1];\r\nx3 = x2;\r\n\r\ny_correct = 0;\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":393995,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-04T14:23:13.000Z","updated_at":"2026-03-19T07:20:29.000Z","published_at":"2020-02-18T12:21:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1.5 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2.7273;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[7 3 11.3];\r\ny=ratio_polygon(s);\r\ny_correct=7.91;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[121 125 17.37];\r\ny=ratio_polygon(s);\r\ny_correct=8.5438;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[19 3 25];\r\ny=ratio_polygon(s);\r\ny_correct=21.5909;\r\nassert(abs(y-y_correct)\u003ceps)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-21T18:12:43.000Z","updated_at":"2026-03-24T12:20:14.000Z","published_at":"2021-01-21T18:12:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a square sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"282\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"287\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the 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many points lie within the rectangle and how many aren't?","description":"Suppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as *input-1, R* i.e *R=[Bottom-left corner co-ordinate; Top-Right corner coordinate]*. And you are told to count the points of the *input-2, P* (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. *Show them collectively within an output matrix, Y.*\r\n\r\nExample: *Inputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];*\r\n","description_html":"\u003cp\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as \u003cb\u003einput-1, R\u003c/b\u003e i.e \u003cb\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/b\u003e. And you are told to count the points of the \u003cb\u003einput-2, P\u003c/b\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. \u003cb\u003eShow them collectively within an output matrix, Y.\u003c/b\u003e\u003c/p\u003e\u003cp\u003eExample: \u003cb\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];\u003c/b\u003e\u003c/p\u003e","function_template":"function Y=PointsWithinRectangle(P,R)\r\nY=1;\r\nend","test_suite":"%%\r\nP =[1 0;1 5;5 5;-1 2;5 -4];\r\nR=[0 0;10 8];\r\nY_correct =[2 3];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 2;-1 4];\r\nR=[-1 2;3 8];\r\nY_correct =[0 2];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 4;2 -4;6,-6;4 5;1 2;8 9;1 1;0 0;-1 -2;4 5];\r\nR=[-1 4;2 8];\r\nY_correct =[15 0];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;2 0];\r\nR=[0 0;10 8];\r\nY_correct =[9 12];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[11 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;22 0];\r\nR=[0 0;10 8];\r\nY_correct =[11 10];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":430818,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2020-05-31T08:14:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-30T08:08:12.000Z","updated_at":"2026-03-31T13:03:03.000Z","published_at":"2020-05-31T07:15:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput-1, R\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e i.e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. And you are told to count the points of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput-2, P\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eShow them collectively within an output matrix, Y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5] Output: Y=[1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54124,"title":"Area of a regular hexagon","description":"Given the length of a side of a regular hexagon, return its area rounded to two decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven the length of a side of a regular hexagon, return its area rounded to two decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hexagon_area(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2.6;\r\nassert(isequal(hexagon_area(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 64.95;\r\nassert(isequal(hexagon_area(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = 259.81;\r\nassert(isequal(hexagon_area(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1985600,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T19:42:05.000Z","updated_at":"2026-03-23T10:21:34.000Z","published_at":"2022-03-04T19:42:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the length of a side of a regular hexagon, return its area rounded to two decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; 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sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n  T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n              3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n              1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-04-17T01:06:41.000Z","published_at":"2025-07-23T16:40:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh, that is to say give one triangulation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"335\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"447\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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the area of the shoemaker’s knife","description":"A shape resembling a shoemaker’s knife is constructed from a semicircle with diameter  with two semicircular “bites” of diameters  and . \r\nWrite a function to compute the area  of this shape as well as the area  of a circle with diameter , the length of the line tangent to the two smaller semicircles and touching the edge of the largest semicircle.\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 399.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 199.85px; transform-origin: 407px 199.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, 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italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.625px 8px; transform-origin: 97.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with two semicircular “bites” of diameters \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a-b\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.608px 8px; transform-origin: 114.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ak\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.85px 8px; transform-origin: 103.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of this shape as well as the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ac\" style=\"width: 16.5px; height: 20px;\" width=\"16.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a circle with diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the length of the line tangent to the two smaller semicircles and touching the edge of the largest semicircle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 266.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 133.35px; text-align: left; transform-origin: 384px 133.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 417px;height: 261px\" 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\" data-image-state=\"image-loaded\" width=\"417\" height=\"261\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Ak,Ac] = arbelos(a,b)\r\n  %  a = diameter of largest semicircle\r\n  %  b = diameter of medium semicircle\r\n  %  Ak = area of the shoemaker's knife\r\n  %  Ac = area of the circle with diameter c\r\n  Ak = polyarea(a+b);\r\n  Ac = pi*c^2/4\r\nend","test_suite":"%%\r\na = 1; \r\nb = 0.45;\r\nAk = arbelos(a,b);\r\nAk_correct = 0.194386045440868;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = 1; \r\nb = 0.37;\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 0.183076311887945;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%%\r\na = 2; \r\nb = 1.1;\r\nAk = arbelos(a,b);\r\nAk_correct = 0.777544181763474;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = 2;\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 1.128274457746991;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 0.45;\r\nAk = arbelos(a,b);\r\nAk_correct = 0.901244392498572;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = pi; \r\nb = pi/6;\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 1.076606829177077;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(17); \r\nb = sqrt(10);\r\nAk = arbelos(a,b);\r\nAk_correct = 2.386357557750292;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(31); \r\nb = sqrt(29);\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 0.772304555883422;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%% \r\nd = [3.5 8];\r\nfor k = 1:4\r\n    [Ak,Ac] = arbelos(d(k+1),d(k));\r\n    w = rand;\r\n    d(k+2) = w*Ak+(1-w)*Ac;\r\nend\r\nd6_correct = 2.568944500499240e+03;\r\nassert(abs(d(6)-d6_correct)/d6_correct \u003c 1e-13)\r\n\r\n%%\r\nfiletext = fileread('arbelos.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-16T01:00:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-16T00:57:58.000Z","updated_at":"2025-04-28T19:56:12.000Z","published_at":"2023-01-16T00:59:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA shape resembling a shoemaker’s knife is constructed from a semicircle with diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with two semicircular “bites” of diameters \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a-b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea-b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ak\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of this shape as well as the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ac\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a circle with diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the length of the line tangent to the two smaller semicircles and touching the edge of the largest semicircle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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ThCCmlAegTQIQAFC+CEIOVGW2hCAm5RwgACA10Z0iCDEbQhATOjx0yjlAAECSIghFtwq0QwhiXBGAnvvV3uIOACA9cWSHIEQ7hCAuEC1wEYBUgACA1EXbfjy7wEwIQVzgb14+IgABAJUQzyzRvq8ixEwIQXwqWuB+9PPd2dHh08U7AADVEBWheJaB6RCC+NQLr34gAAEAlRQVoWjn1xrHdAhBnBuCsHFf9v6hE8U7AADVE0Eo2vpVhJiKEET2D28MCEAAQC1EV8v6l94ThJiUENRwUQHatmuouAMAqL4IQtHmDxMRghps4+YPVYAAgFqKZ5w4RwjGIwQ11JbtR7LXdhwp7gAA6ifGZm96/XBxB58RghrozT0fZb/Z+mFxBwBQX5u2DeSLvzCaENQwMTby+VcOFHcAAPUXi78OU2U0IahBhk+cyZ55caC4AwBojtgf5AwhWoSghogA9NzGvfn8fACAJorF4HgmAiGoIWJMZIyLBABoqlgMjkVhQQghqAFiFLY+WACAc2cI/ezl/cUdTSUE1ZxR2AAA54szhH7pMNVGE4JqzChsAIDxbds1ZHR2gwlBNRXTTzZuPljcAQAwViwWC0LNJATV0OGhU/n0E5PgAAAm5wyhZprzyVnFNTXx3MZ9ea8rQB1t+Kv/mP3u1ReyU6dOZoc/2JutuPq67J9++Z7sa9/4TnbJoiXFf6rzvvftG/LXp376dv4K1MeC+RdlD921LOvv7y/eoe6EoJoRgIC62r19a/bDf//d7Pjw0eKd882bvyD71//r/5VdefX1xTudJQRBvX3u8r7sgbuvLu6oO+1wNbLp9cMCEFBbowPQ1/7b/z777r9el/3Zv/vr7Cv3/Iu8AnT61Ej2m5//H/nvA8xUPEOtf+n94o66UwmqiZgE9/wrB4o7gHr5q7/8n7KXX/g/8+t/9f3/lN1w6x359Wjxn7l57Vez3/vyPcU7naUSBM3wtbVXZLfduLS4o65UgmrAJDig7loB6OrV/2TcABT+5E//l64FIKA5DEpoBiGo4oZPnMl+sXnYJDigtmIvUMtX7nmouALonlhcjmcs6ksIqrhXtg3YBwTUWkyAa7l69S3FFUD3HB0+nf3s5f3FHXUkBFVYDEJ4bYcDvoB6O/DeO8VVll2ycHFxBdBd7+4/km3c/GFxR90IQRUVvaqbtg0UdwDNcPzYUHEF0F0xdj8Wm2P4FPUjBFVQDEJ4fpNJcEAzrLjquuIqy/bt2lZcAfRGTN+NZy/qRQiqIIMQgCa57MpriqsIQW8UVwC98zcvH8kOD50q7qgDIahiojfVIASgSVbduDZvSwmtUdnj2bfrv2Zvv/5KcQfQOTEo4T9vtT+oToSgComeVIMQgCb61nf+bXGVZU9874+y48NHi7ssv97wV/8x+w//5pvZlpf/7+JdgM6K/dgGJdTHnE/OKq5JWPSi/viFQ8UdQPNE+Plg347iLsuuvPr6bGjw4HmBKA5M/co9/6K466zvffuG/PWpn76dvwLNdP9XP5etXrmwuKOqVIIqInpRAZrs8ad+cV7AiUDUCkCXLFqS/dGf/A9dC0AALetfet+ghBpQCaqA5zbusw8IoBDBJ9//s+2VbEn/FdkNt9yRV4UWzL+oq0NjVIKAls9d3pc9cPfVxR1VJAQlLg5EdR4QQPmEIGC0L16/NLv79iuKO6pGO1zCHIgKAJCmGFYVz2pUkxCUsI2bDxZXAACkJp7VnB9UTUJQon756gf5THoAANIUz2r/8IaunSoSghIUpdVtu4aKOwAAUhXPbFu2m+JbNUJQYmLk4vObDhR3AACk7jdbPzQ2u2KEoMT8P1uPdXXEKwAAnfeLzcPZ8IkzxR2pE4ISEqXUvQePF3cAAFRFnOn4jzu0xVWFEJSImCwSpVQAAKopjjZ5c89HxR0pE4ISEKXTF179oLgDAKCqfvu7Q9riKkAISkCUTqOECgBAtcXY7J+9vL+4I1VCUMliHHaUTgEAqIdY3DY2O21CUMmMwwYAqB9js9MmBJXouY37jMMGAKipGJtNmoSgksTkEPuAAADqK571Nm42/TdFQlAJojT6/Cva4AAA6u61HUfyo1BIixBUgpe2qQABADSFo1DSIwT1WLTB7dinPxQAoClMi0uPENRjGzcfLK4AAGgK0+LSIgT10PqX3jcNDgCgoWyJSIcQ1CNxKGr8AgCgmWJLhLa4NAhBPTB84ow2OAAAsk2vH86fDSnXnE/OKq7pkvjLvmnbQHEHE/vc5X3FVZatWnFJdmzk42zhgovy12WL5+e/OmVg6FQ2cvJM/t8dDg6O5K/BGVZwoe99+4b89amfvp2/ArRr9cqF2f1f/VxxRxmEoC6LDXA/fuFQcUdTLVk0L1vUNy8PNmFlEXb6+05m/f39+XWq4myDo8Pnzjd4571jeSjbfeB4fi8s0SRCENBJ992xIrvp2kuLO3pNCOqy5zbu86DYAAvmX5RdtuTiT6s31121MH8/VnqaIML+4ImL8+pS/Iqq0uGjJw0CoVaEIKCT4tnhkfvXFHf0mhDURbHxLcYhUi9R1Vm9ctGn7WlNCTrtioEgrWAUrxYFqCohCOi0W1Yvzr7+5SuLO3pJCOqSaCH6yYY9xR1VFXt0lvcvyK6+oi9bseR08q1rVREbQiMURXtdvApGVIEQBHRD7A2yoNp7QlCXaIOrpvgQWnX215rlnwg8PRYtdTsPzsl27z+WHR46mR0dPl38DqRBCAK6ITpMvvuNVcUdvSIEdcGbez7Knn/lQHFHquJD55rll+SVngg+l3Vw8hqdEf+W9n14Itu1f1goonRCENAtX7x+aXb37VcUd/SCENRh0eYTbXA2hKcpem8j9Nx249LiHaok9tlF+9y2XUPFO9A7QhDQTd+553JdKD0kBHXYL1/9wANaQlp7em6/bp4Plppptc9t2T6oSkRPCEFAN8UzywN3X13c0W1CUAfFFKz1L71f3FEW1Z7miQrsW+9+pEpEVwlBQLc5O6h3hKAOMgyhPBF8vvD5S01XIRd7iXYfOCYQ0VFCENBtsV/5gbuvyRb1zS3eoVuEoA4xDKH3IvisWrHQigmTagWiHfuG7dVjVoQgoBe+tvYK3Sw9IAR1yLr1Oz1g9UD0y669YangQ1uiZTXa5lSIaIcQBPSKIQndJwR1wMbNH2av7ThS3NFpgg/dEIHolW0DWliZNiEI6BUjs7tPCJqlmFD14xcOFXd0yoL5F50NPYtNdaPrDg+dyg9o3fT6YdVcJiUEAb10/1c/Z69zF11UvNKmze8YzdtJUfWJySiP3L8mXwERgOi2OCQ3eq/j71z83fOFA0AKoluB7lEJmgUjsTtD1YfUtM4gUh1iNJUgoNcMSegelaBZkNBnJ8ZAqvqQovi7OLo6FBVKAOi1WIyjO4SgNsXYXRuq2xMPlNHn+t1vrDLsgOTF39E4wTsm9WiVA6CXohshBnDReUJQG2Ij9cbNB4s7pivO9fmX916bP1B6mKRqojoU4f1Pv7k6n9oDAL0QE4iHT5wp7ugUIagNMUnKPoHpif0+8cAYD45f//KV+SZ0qLI4xTvaN//sT67Pe7Xj7zgAdNPPXt5fXNEpvr1nKDZM/2arsuRU4sEwHhBb+33iwRHqprVvSBgCoJtiC0YM5KJzfGvPkJHYkxsdfkwzoSmEIQC6zVaMzvJtPQORwKMvk/EJPzSdMARAtxwdPp1t2e45tFN8S8+ABD6+O29Zlu+PEH7gnNFhCAA6JUZmG5LQGULQNMVI7EjgfCYGHkT4ufPWy4p3gNEiDLUGKADAbMVgrrfe/ai4YzaEoGn67e8OFVfEqOt4sIuBB8DUWmHIaG0AZuP0qRHVoA4RgqZBFeicOOQ0zvmJUdfAzMXCQYyLj39LADBT8+YvUA3qECFoGqIKFMm7qWKDdxwSGYecOucHZifGxce/pfg3JQwB0A7VoNkTgqbQqgJF8m6i1sS31SsXFu8AnRD/piIM3XfHCpPkAJgR1aDZ8807habuBWrt+zHxDbrrpmsvNUkOgBmxN2j2hKBJNHEv0JJF87Lv3HO5fT/QY7HgEHvutMgBMJXW3qB/dH5l24SgSTRtL1CsRH/3G6uy/v7+4h2gl2LPXWu/EABMZdO2gWxwcLC4YyaEoAnEibxN2QsUK89a3yAdsV8o/k3aiwfAVDa/Y4JxO4SgCUSfZd3FZuzYlB0rz0B6oiIU7akGJwAwkdd2HMkOD50q7pgu36zjiAAUfZZ1FivMsRk7NmUD6Yr21Pi36qBVACaydbu9QTMlBI0jWuHqqnXmjz0HUC1x0GpUhWJ4CQCMFtUge4NmRggaIx83eOx4cVcvsZLszB+orqgKxfASVSEAxrI3aGaEoDGiClTHYQhR+YmVZKD6WlUhAGixN2hm5nxyVnHdeFEFilGDdRKT3ww+gHqKQ/J++4+Hsm27hop36KbvffuG/PWpn76dv0I3jD4rbNWKS7JjIx9nyxbPz391wjvvHcsWLrgo/+89febjbGDUQ/P7h04UV1RVdApY9J4eIWiUdet31mogQpz7Y+w11F9UsH+z9cPijm4RgpitVsBZ3r/gvGCTWpt67C0ZPHFxHpBGTp7Jdh84t01ASEpf7P1+4A+vyc+dY3JCUCGqQP/l/9tfi1a4+Afw0F3LHHoKDRJVoec27s3PN6M7hCCmK8JOBJxW2KnbXtxd+4/lAeng4Ej+KhylRTVoeoSgQl2qQP7iQ7PVsa03FUIQY8Wi42VLLs7DznVXLcz6+042dgEyFmJaoeitdz/KDh89WfvjRlIWB24zOSHorLq0ksTBp879AWKV9vlNBzyAdJgQRISe669elIeeNcs/0XExhWir23lwTh6M3twz5DOph2yJmJoQdNZzG/dVupQb54b88VeW+jAGzvOjn+/WHtdBQlDzROi56drF2dVX9GUrlpz2PdsBb+75KNt94Fi2Y9+wUNQlp0+NZIsWXpL9y3uvzRb1zS3eZazGh6D4x/h3/2VPZfcCmf4GTOaXr35gelyHCEHNEN+rX/j8pSo9PdCqFEX7nH1FnadDaHKND0HrX3o/bx2pIqVOYDpisef5Vw4Ud7RLCKqnVovbqhULPTCWLJ7HIhCpEnVGdArFAduMr9EhKFYgfvzCoeKuWuLw07pNmwG6Jz7v/ublI9rjZkEIqo9W8Pn9Gy9W7UlUfGZtfue0vUSzpBo0sUaHoI2bP8xP162SSPX3f/Uq89+BtlR9D2SZhKBqawWfaHWziFgtEYj+3+0nVYjaYNvExBobgqpYBYoP7agAAcyGw1XbIwRVUzwE3nHLMsGnJlotc/Y6Tt937rlcxXMcjQ1BVXsIsP8H6CRBaOaEoOqIqk98Z/7e9UtNx6qx2O/4298d0uY7BdWg8TUyBMWBXn/5d7uKu/QJQEA3OE9oZoSg9Kn6NJP9Q1P702+utiAwRiNDUJVWQA1AALrp8NCp7Llf7fXgMA1CUJpaZ/ncffsVxTs0WVSHNm4+6DNtjFtWL86+/uUrizvCRcVro2zZPlhcpSs+1OOQKwEI6KYYsvLI/WvyFXSokviejE6J+PsrANESk9Di70RMRYthUpxjD9WFGheCYoUg9d7R+EcbAcgEOKBXol/cogtVMDr8aBVnIhGG4oyc6KixyJNlp0+NZJteP1zcERoXgra+nfZI7PiHGv9o9W0CvRYPC3fesqy4g7TEAmGs7gs/zEQs7sQiT9PD0Lz5C/LtIHymUSEoNs6lfD5G9Gua3gGU6c5bL8tX2SEVrfATC4QOfaRdrTAU46KbGoZin5Qg9JlGhaCXtqUbgL54/VIb1oAkxCq7IETZhB+6Ic7LiTAU2w5i8blp4owlzmlMCIoJSHHScIqi/cSmTiAlEYTiARR6LVbpo3VJ+KGbYt91LD5HZahJYejd/Ufy4xFoUAh6a0+aUzFitTXaTwBSEw+g8TAKvdAKP4Z00EtRGYowFOfoNKFNLvYGvfOeEBQaE4JS7IGMAGRzJ5CyeBgVhOimmPYWVUfhhzLFQKrWnqH4O1lnr+2wLyg0IgRF2S+1Q7MEIKAq4sE0Hgyg02I/bEx70/ZGKqIyFH8n674v0oCEhoSgrYn9QQtAQNXEg0FsJIZOiKEHEazthyVV8Zz2Z39yfS1b5OLMIAMSGhCCYix2ShvAoq1EAAKqKDYSqwgxW7EQGEMPIlhD6qJFLp7d6tQiF/uC4siYeEZustqHoJ0H5xRX5Yt/RPqdgSpTEaJdMYErVtYtBFI18exWxxa5ze+cLq6aqfYhaMv2NFJu/MMRgIA6UBFiJqL1LRYBnYVH1UWAj8++669eVLxTbU0fkFDrEBRtcEeHy0+59gABdRMVIVPjmEqr9c0iIHURn33f/MrK2rTINXlAQq1DUApz0AUgoK7iwVYQYjyxmVzrG3XWapGLA++rLJWOqTLUOgSVXeaL0Z++AIA6E4QYq3XmDzRBHHhf5apQdEw1dUBCbUNQ2eW9CEBGfwJNEEGobhuGmbnY+xPVH2f+0DStqlBVx2k3dUBCbUNQmfPPYwKOAAQ0SVS9BaHmiu+92PsDTRYV0Cp+Dr65ZygbPnGmuGuOWoagGIjw7v5yKkGxCmACDtBEEYSiCk6zRPub7z04Jz4Hq9YeN3Lq42zvB8eLu+aoZQiKgQhxEFSvRQDSBw00WVTBoypA/cV3XpwZpf0NzlfF9ritbzdvSlwtQ1CU9XotEr8ABJDlVYHYH0J9RdCN77w4MwoYX5Xa494/dKJxAxJqF4JiIEKU9XrtobuqPSIRoJNif0gdztDgQtrfYPqiPS4OWK3C52HTBiTU7huqjIEI0fsZh2cB8JlYHBKE6sP0N2hPPCNWoT2ujE6qMtXq2ynKeFHO66VYEYveTwDOF1/8quT1YPobzF7q7XHRSRXDxZqiViHojX29bYOLKUhWxAAmFkHIYarVpv0NOif19rgYLtYUtQpBuw/0brxfVH+cBQQwNYepVlM8pMXDmsU+6KxYHHrgD69JMgg1qSWuNiGol61w0RdtZRNg+mL1U+twdcTDWYy/tt8VuiMmK8Y+odQmaUZLXFOmxNUmBPVqokV8Mdz/1auKOwCmKxaPjM5OX/wZxcPZor65xTtAt8Reu9QGJry0rbf768tSmxB0cHCkuOqu++5c4VwEgDZZREpbPIwZgAC9FQMTUgpCez/o3faSMtUiBB0eOtX1VrjTp0bynnbtHADti0Uk7cRpiocwh35DOeLfXkxhTEFTpsTVIgS91YNNXJ9fuTTvaQdgdmIx6c5bjM5OSfyZCEBQrpjCGAvusfBetiZMiatFCNq2u7shKPYB+XIA6Jw7b70s+YMDmyKOe1CdgzTEgvsffrn8Z87Xdhwpruqr8iEoJlgcHe7uUASH/QF0XiwupTgitkmiIue4B0hLBKEUFibq3hJX+W+fnQfnFFfdEWVJI0IBusMiU3ni+y0qckB6okU1zukqS7TkvfXuR8VdPVU+BG3Z3r1Z5rFBzT4ggO6JRSYHqfbefXes8P0GiYvPxzivq4yK+bz5C7Jtu+p9cGqlQ1BMhetWK1z8hYsNagB0VzyM2x/UO9Fmc9O1lxZ3QMpiouYDf3hNaa3Db+6pbzWo0iGom1PhtGgA9I79Qb0RAchRD1AtEYTKei7dfaC++4Iq/Y3Tralw9gEB9F4cRk33xHebAATVFM+lZQxLiJa44RNnirt6qWwI6tZUuCWL5umTBihBPKDHuGY6LwKQ7zaotviMLCMIHRws/9yibqhsCOrGVLhoxbj/q1cVdwD0WoxrjsUoOseQH6iPCEK9HCZT5ylxlQ1B3ZgKF6NCo+8SgPL88Vc8sHdKBCBDfqBeYlEjglAElG6LKXE79g0Xd/VSyRDUjalwVsoA0mBsdmfExD0BCOopnllvv7k3/75HTn1cy4NTKxmCdnf4D8I4bIC0xBe8sdnti5bCmLgH1Fe0D8cifi/sP3SiuKqPSoagTvcmmkgEkJ57LE61JRb2vvuNVcUdUGexiN/tBaNou9t94HhxVx+VDEHvdzCNxgYzI0MB0hN7NLXFzUwEoDhhHmiOqPp2MwjFvqBOPnunonIhqNM9iWWMGgRgeqItzrS46YsDFRf1zS3ugKaIINTNz8qoBm3ZfqS4q4fKhaBOtsLdd4c2OIDUObpgemJRz0Hf0FwxWbNbQSiqQXU7L6hyIWhg6FRxNTtRNrzp2kuLOwBSFW1xDlGdXAQgrd3QbLEI0s1Fo227hoqreqhUCBocHOxYT6KpOQDV4RDViUVAFICA0O29lHUalV2pELTz4JzianZstAWoHoeoXii6GiIgArTEXspujc7u9ITmMlUqBHWiFS6+MByKClA90eqhLe58uhqA8cTo7JgW2Wmd2paSgkqFoNd2zH4qxR/dvqi4AqBqVD0+Y7gPMJmYFtlpsS0ltqfUQWVCUCd6EGMF0eQcgGrT0pzlrS6G+wCTiWfebnxeHjhaj/2ZlQlB+zswEMEKIkD1Nf3soPj/e7S6AEylG/uDtr5dj/OCKhOCdh84nh/U1C4rhwD1cffty4ur5nng7muKK4CpdXp/0OGjJ4uraqtECBo+cSbvQYyDmtoRq2aGIQDUR4yEjkE3TRP7gBb1zS3uAKank/uDRk59XItR2ZUIQbMdx/fP/+nlxRUAdXFPw1rC7AMC2tXJ/UHRmdWJbSplq0QIOjjYfhtcrBT60gConzgUsFtnYaQkHjjiu8w+IGA2OrU/KDqztu0eKu6qqxIhaMe+4eJq5ozEBqivbp2FkZJ44Gha1Qvojk59Zh4dPl1cVVfy3xwxizx6D9thJDZA/d1562XFVT3FPqCoegF0Qqf2B725Z3bbVcqWfAjaeXBOcTVzd9zS+UOiAEhLnUdm2wcEdFqn9gcNDFV7SlzyIWhg6FRxNTPxh2uCDkAz1HEATrSs2AcEdMNsF49ir2IcX1NlyYeg13a0dyCTkdgAzRHVkrpVg+re5geUazbnrcVexaqfF5R0CIrzgdrhYFSA5qlLNag1Dc5iHtBNcd7abKbFxZ792LtfVUmHoL0ftFdm88UB0Dx1qQbFCqvJpkAv/LObl81qWtwb+9obXpaCpEPQvg9nfhCTKhBAc9WhGmSyKdArMXlyNq23R49Vd1R20iGonUNSVYEAmqvq1aBYkb37dot5QO/Es3O04LZjNmd5li3pEPT+oZlVglSBAPjjr1R3McwwBKAM7bbgVnlfULIhqJ0DmFSBAIhWsnZXNctkGAJQlvjcjFbcdszmTM8yJRuCjo3MbDKcKhAALVUcLGAYAlCmaMVtZ0hCu2d6li3ZEPTWuzOrBFk9A6AlVjWrtDfIMAQgBe205O7aX819QcmGoJkcwKQKBMBYVZoUZxgCkIJ2hiQcHT7d9tmeZUoyBMUGq9hoNV1rln9SXAHAOVWZFHffHSuKK4DytdOa285E57IlGYJmssFKCwEAE7ntxrS/H2LFNcIaQCraGZLwznvHiqvqSDIEzWSD1e3XVf90cAC6I/X9ooYhACm645ZlxdX0qAR1SGywOn1q6h9mrKCpAgEwmVT3jfoOA1K1qG/ujKpBMz3bMwXJhaDDQ6fyDVbz5i8o3pnYTFMqAM2T6r5RVSAgZTN5zo7iRdUOTU0uBB0cmF45LTa7rl65sLgDgPG109/ebdcsv0QVCEhaVINuWb24uJtcFC+qdmhqciFoYGh6o7GrNPoUgHKl1jnw36y1iAek75//3vSft0dOVmtMdnIhaP/hqStBcZqtaToATFesaM707ItuUQUCqmIm1aDdB44XV9WQ4J6gqStBN107vT8MAGhZe0MaLXH/7GYBCKiOr3/5yuJqcoePTq+bKxXJhaAYijAVAxEAmKnoIIhOgjLZzwpU0XSqQSOnPs6GT1SnJS6pELRr/9QHLUU7Q5TmAGCmyu4ksJ8VqKLfv/Hi4mpyVTovKKkQNHLy4+JqYqpAALSrzAO2owpkPytQRbGPcap9lTEme2DoVHGXvqRC0O4DU1eCtBEA0K7pfJF3iyoQUGVTnW0WY7KFoDYdm6KPMLVzHgConjIGJKgCAVU3nUWkN/cMFVfpSyoEvX/oRHE1vjLbGACohzLCyG03mggHVN8905wUVwVJhaDhYxPPF4/k6VwFADqhl50FMZHutht1MgDVd9ni+ZNWg2JC3ODgYHGXtmRCUEyGi17CiaRyvgMA1dfLzoI7b72suAKovqmGlO08OKe4SlsyIWiqjVR6qQHolOgs6NWZQapAQJ3EkLLJPj+rMhwhmRA02Vzx6RzQBAAz0YsKje8voI4m+/ysyllBlagEfeHzqkAAdNaqHhy5MN0DBgGqZLIK9+GjJ4urtCUTgiabDOdsIAA6LTb4xujqbon/bgN9gLqaaEBCDEeogiRC0PCJM/kps2PFe1oJAOiWbo6uNhYbqLPJBiS8ueej4ipdSYSgvR8cH3cyXLynFQ6AbulmS5yBCECdTTYg4djImeIqXUmEoMl+UFrhAOiWbrXETXWqOkAdjDcgITq5qjAcIYkQ9Na745fMtMIB0G3daFub6hwNgDpYs/yT4uoz0clVhTHZSYSgiaxaoQoEQHd1uu062kN0MQBNEMNfqlr5TiIETTRKzwGpAHTbor65Hf0Sv+laXQxAc4y3kDTZ1OdUJBGCho8dL67OMRUOgF5ateKS4mr2rrtKFQhojokGzAwODhZXaSo9BMUPaOxkuLhf3n/htDgA6Iabr+7M16FWOKBpYsBMFVviyg9BJ8Y/TdtoUQB6JfraJxr1OhPXX72ouAJojrU3XPjcvvPgnOIqTaWHoPGmR3TzBG8AGE8n9vI42w5oolVXVu/ZvfQQNHLywjOCblllPxAAvXX1FbNr59AKBzRVX1/fBS1xqY/JLj0E7T984WFKKx0yB0CPXXPl7IYjmAoHNNnYlrjUD0wtvxJ06uPi6txUOCtpAJRhtqOyTYUDmmz5sgX5s3zLREfgpKL0EDT6BxRT4WwqBaAss9nTYwEPaLKYEndZ/2fP8aMLHSlKqhIUjMYGoCzL+8efWDqVqp6YDtBJq1eeX8xI+aygUkPQeD8Yo7EBKMs1yy9pa1S2qXAAF7YFT3QUTgrKDUFjfjBW0gAoWzsDDiY6MR2gSca2Bac8Ia7UEDT2B6MVDoCyLVwws6/GONsueuEBOL+oIQRNYOwZQbM9owEAZusLM6wEje2BB2iy0e3Bp8+kOxyh1BB09Njp4uqcm67VUw1AuWZa1bGAB/CZNcs/Ka5UgiY0+gfTzkZUAOiGmexRtYAH8Jn+/v7iKu2zgkpNHqN/MM4HAiAVq1ZcUlxNLvYDAXC+1kJSymcFlbsnaNQPxlAEAFKxcpqVIPuBAC40el9QqmcFlRaCxv5ARvcPAkCZxo55ncgyU+EALjD6s/HjuWkuFpUWgsb+QEb3DwJA2abT6uZ8IIALjV5IOjqc5nCE0kLQwYGR4sohqQCkZ6pWtxjo43wggPF9ui/oZJr7gkrdE9Qyum8QAFIw1ehrC3gAE2s93x8bOf9c0FSUFoJG/0D0VAOQmuXLJh/YoxUOYGILF8zNTp/6rPMrNUlUgvr70p0hDkAzTdXqZgEPYGIrlpzO5s1fkB0cTDMIlRaCWgelRk+1oQgApGiylrfpTpADaKLW8/28uUnUXC5Q2v+q02fObZK6bMnF+SsApGaiM+xiAQ+AycVCkkrQGK1KkENSAUjVRC1vvrsAppbyZ2XpS1l6qgFI1UTfUboYAKYWn6GHj6a597+0EDR84nT+umb5J/krAKRmon0/FvAAphbP+SOnnBM0LkMRoH2PPPJIdtttt2Uvvvhi8Q7QaePt/zEeG2Bq8/sWF1fpKS0EHR4czpYsmlfcAe14+umns61bt2a/+MUvineAThuv9W2q8dkAZNmivrn5QtLg4GDxTjpKC0ExN3xRnxAEQNpap563mAwHMH2xkDR4Ir19lKV8krfS4NgvFqA9CxaYVAW9YjIcwPSl+plZSgj66JQvEOikkZE0Z/BDHYzd/2MyHMD0LVxw0adH46SklBB0+sy5iXCm60BnqARB7/juApi+BRfPLa7SUkoIGjl5blTekkW+SKATVIKgewxBAGhfLByNnDxT3KWjlBB0bOTcD8IXC3RGqxK0fv36fGT2nDlz8l9x/YMf/CDJqSxQJaOHIRiPDTB9/X0OS/1UpEHTdaBzohIUZwZ961vfykdmt8T1448/nochQQjaZxgCQHviTNBjI+kdmFpSJehjG0uhg+K8oPgVHzTr1q3LtmzZkj3zzDPZnXfemf/+rl27soceeii/BmZu9HeWLgaA6pvzyVnFdc9s2X4kOzg4kn39y1cW7wDtiJa3lrVr1+bhZ6yoArWqQ/H78Z8DZia+t27/Qn9+XcLXJkClbXr9cHbnrZcVd2kopRIUAWjJQgelQqdEsPn7v//74u583//+94urLPvhD39YXAEA9EaKE+JK25iT6rg8qKJ777036+vrK+7Od//99xdX59rigJkzDAGgXkoLQQsXCEHQKytXrsxf33jjjfwVAKDJSglB8+ZelK1Ycrq4A7qttQ/oxIkT+SswM4YhANRLaXuCYooV0BlLly4trsbXqgC1KkIAAL0SB6amppQQ5LwF6KwjR44UV+NrnRF08803568AAE1WWiUI6JzJBh7EeOxWCFq9enX+CkxPHEIcY+bvu+++4p1zY+e/+Ptfd/YWQIWVEoJSLIlBlT377LMTPpA9/vjjxVWWPfDAA8UVMB1f+9rX8oWEDRs2FO+cW1j4x1dfyL70pS8V7wAwmf6+k8VVOkoJQUDnRRCK1erWwahR/YkA1Hp4izHaDkqFmXnwwQfH/XcT+1ofe+yx4g6AyczvW1xcpUMIghqIh7F4KIvAE606y5Yty3/94Ac/yH8/2uDWrVuXXwMz8+ijjxZXn3niiSeKKwCmcurEUHGVjjmfnFVc98yW7Uey226cfJoVMLU5c+bkr1u2bMlD0Le+9a1PK0EtsZIdAchERmhfLC60/m3Fv6WBgYH8GoCpHR46ldxRA0IQVFhrIMLogQfxoNYahHDXXXflr8DsrF+/Pl9kCFEF0goHUG1CEABMw5o1a/IFBlUggOorZU/QwgVziysAqIannnoqe/Tx/7G4A6DKSqkEvbnno+ymay8t7gAgfXsPHs8W9s1Lrq8dgJkrpRK04GJD6QColghAANSDNAIA0xAVIFUggHooJQSt7Je9AACAcpSyJwgAAKAsSjIAAECjCEEAMMojjzzy6UHEANRTUiEovnR8+QBQpmeffTY/GPWhhx7yfQRQU0mEoFb4iS+dp59+ungXAHqvv78/fx0dhrZu3Zq/B0A9lDoYYf/+/dmf//mfXxB8du7cma1evbq4o4kGBwc9dCQu/oxeeeWV4o4UxZ/Rpk2bijumY+XKldmGDRuKu/Pde++92RNPPJGtXbu2eAeAqiolBEXl58knn5yw6tOLLxgP2ADMRFSIHn300eyxxx4r3gGgqkoJQdFi8Pjjj+u1ZlIRhmNVNiqGXtN7bf0ZLV26NDty5IjXBF9DVC+iIhQP8CdOnMj6+vq8TvDa+jn9wR/8QX7dIvwA1E+p7XBRCYqK0Ngw9Mwzz2Q333xzft36UurUdetVOwMA41m2bNmn3xXCD0A9JXFY6o9//ON8b1ArDNkTBEBZbrvttuyBBx7IHn744U8X0gColyRCUEurMvTrX/9aCAIAALoiqRAEAADQbUkdlgoAANBtQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoQhAAANAoSYWgXbt2ZQ899FBxBwAAVEE8w8ezfFUkEYJa4WfNmjXZs88+W7wLAABUQTzDx7N8VcJQqSFI+AEAgPqoShia88lZxXXPxA/k8ccfF3wAAKDGHnzwweyJJ57IVq9eXbyThlIqQRs2bMh/AQAA9ZXqc38plaCWqAQ98sgj2eDgYPHOOSX+TwIAAGZozpw5xdU5UfmJClBUglJU6p6g+KEMDAxkzzzzTHIlMgAAYGbimX7dunXZzp07kw1AodRK0FhPP/109uSTT+Y/NAAAoBpiGMKjjz6aPfzww8U7aUsqBAEAAHRbUoelAgAAdJsQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANIoQBAAANMqcT84qrgGg4wYHB7OtW7dmb7zxRn5/8803Z2vXrs36+/vzewDoNSEIgK548cUXsyeffDLbsGFD8c75HnvssezRRx8VhgDoOSEIgI7btWtXtmbNmuIuy+69995s//792cqVK7NNmzbl1aHW+88//3x+DQC9Yk8QAB0XQSc88cQT2cDAQB50tmzZkr/u3Lkzb4cLUSWKwAQAvaQSBEDPxR6h2267Lb9et25d9vDDD+fXANALKkEA9Nzq1auLqyzbvXt3cQUAvSEEAdBzhiEAUCYhCICuevrpp7P77rsvb3+LYQlz5szJfwFAWYQgALoiwk+EnUceeSQfgBD7gAxBACAFQhAAHffss8/m4SfEJLhf//rXWczhGf2rZenSpcUVAPSGEARAx/3t3/5t/hp7f2I09l133ZXfj+fIkSPFFQD0hhAEQMdFJSjceeed+SsApEQIAqDjWiOwW4emjvXQQw8VVwDQe0IQAB1377335q+Dg4N54HnxxRfz66gQxZS4VqUo2BMEQK/N+WT07lQA6JAYhz3RNLiHH37401D02GOPZU888UTxOwDQfSpBAHRFDESIsNNqjYshCQ8++GA+KW7dunXZl770pXzPULwCQC+pBAEAAI2iEgQAADSKEAQAADSKEAQAADSKEAQAADSKEAQ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lines","description":"Check whether two given lines are orthogonal or not.\r\n\r\nTwo lines are orthogonal if they create a right angle at their intersections.\r\n\r\n* p=[x1 y1; x2 y2]   \r\n* q=[x3 y3; x4 y4]\r\n\r\nhere (x1,y1) and (x2,y2) form a line.","description_html":"\u003cp\u003eCheck whether two given lines are orthogonal or not.\u003c/p\u003e\u003cp\u003eTwo lines are orthogonal if they create a right angle at their intersections.\u003c/p\u003e\u003cul\u003e\u003cli\u003ep=[x1 y1; x2 y2]\u003c/li\u003e\u003cli\u003eq=[x3 y3; x4 y4]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003ehere (x1,y1) and (x2,y2) form a line.\u003c/p\u003e","function_template":"function tf = ortho_line(p,q)","test_suite":"%%\r\np=[7,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,3;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[2,2;5,5];\r\nq=[0,-2;-2,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-26T06:07:02.000Z","updated_at":"2026-03-05T16:46:12.000Z","published_at":"2020-01-26T06:07:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck whether two given lines are orthogonal or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo lines are orthogonal if they create a right angle at their intersections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=[x1 y1; x2 y2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=[x3 y3; x4 y4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere (x1,y1) and (x2,y2) form a line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61303,"title":"Steering 101-Ackermann Steering Ratio","description":"In a turning vehicle, inner and outer wheels follow different radii. Ackermann steering geometry ensures both wheels roll without slipping.\r\nGiven wheelbase L, track width W, and outer wheel angle δo, compute the inner wheel angle δi \r\nusing:\r\n\r\nYouTube concept reference","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 140.883px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 70.4297px; transform-origin: 467.496px 70.4414px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a turning vehicle, inner and outer wheels follow different radii. Ackermann steering geometry ensures both wheels roll without slipping.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven wheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, track width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and outer wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, compute the inner wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδi\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eusing:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"192\" height=\"18\" style=\"width: 192px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003ca target='_blank' href = \"https://youtu.be/i6uBwudwA5o?si=AkGgaHat1SAAMDjJ\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eYouTube concept reference\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function di = ackermannInnerAngle(L,W,do)\r\ndi = 0;\r\nend","test_suite":"%%\r\nL = 2.5; W = 1.5; do = 20*pi/180;\r\ndi_expected = atan(1 / (1/tan(do) - W/L));\r\nassert(abs(ackermannInnerAngle(L,W,do) - di_expected) \u003c 1e-6)\r\n\r\n%%\r\nL = 3.0; W = 1.6; do = 15*pi/180;\r\ndi_expected = atan(1 / (1/tan(do) - W/L));\r\nassert(abs(ackermannInnerAngle(L,W,do) - di_expected) \u003c 1e-6)\r\n\r\n%%\r\nL = 2.8; W = 1.4; do = 25*pi/180;\r\ndi_expected = atan(1 / (1/tan(do) - W/L));\r\nassert(abs(ackermannInnerAngle(L,W,do) - di_expected) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:12:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:11:44.000Z","updated_at":"2026-04-29T23:14:52.000Z","published_at":"2026-04-28T09:12:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a turning vehicle, inner and outer wheels follow different radii. Ackermann steering geometry ensures both wheels roll without slipping.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven wheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, track width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and outer wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the inner wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδi\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eusing:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta i = atan( L / ( (L / tan(\\\\delta o)) - W ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/i6uBwudwA5o?si=AkGgaHat1SAAMDjJ\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eYouTube concept reference\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44060,"title":"Volume Pillar","description":"Calculate the volume of a pillar with radius l and heigth ar.","description_html":"\u003cp\u003eCalculate the volume of a pillar with radius l and heigth ar.\u003c/p\u003e","function_template":"function y = Pillar_Size(l,ar)\r\n  y = x;\r\nend","test_suite":"%%\r\nl = 1;\r\nar = 2;\r\ny_correct = pi*2;\r\nassert(isequal(Pillar_Size(l,ar),y_correct))\r\n\r\n%%\r\nl = 12;\r\nar = 25;\r\ny_correct = pi*3600;\r\nassert(isequal(Pillar_Size(l,ar),y_correct))\r\n\r\n%%\r\nl = 6;\r\nar = 2;\r\ny_correct = pi*72;\r\nassert(isequal(Pillar_Size(l,ar),y_correct))","published":true,"deleted":false,"likes_count":15,"comments_count":1,"created_by":99516,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2146,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-06T15:36:59.000Z","updated_at":"2026-04-30T17:09:36.000Z","published_at":"2017-02-06T15:36:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the volume of a pillar with radius l and heigth ar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44276,"title":"Simple spirometer - find your lung capacity from the number and size of soap bubbles in one breath","description":"Assumed that each bubble has practically the same diameter d. Given total number n of bubbles. Find volume v of breath. ","description_html":"\u003cp\u003eAssumed that each bubble has practically the same diameter d. Given total number n of bubbles. Find volume v of breath.\u003c/p\u003e","function_template":"function v = spiro(n,d)\r\n  v=n/d;\r\nend","test_suite":"%%\r\nn=10;\r\nd=6;\r\nassert(spiro(n,d)\u003c365*pi)\r\n\r\n%%\r\nn=10;\r\nd=6;\r\nassert(spiro(n,d)\u003e355*pi)\r\n\r\n%%\r\nn=125;\r\nd=1;\r\nassert(spiro(n,d)\u003c25*pi)\r\n\r\n%%\r\nn=120;\r\nd=1;\r\nassert(spiro(n,d)\u003e19*pi)\r\n\r\n%%\r\nn=12;\r\nd=1;\r\nassert(spiro(n,d)\u003c3*pi)\r\n\r\n%%\r\nn=11;\r\nd=1;\r\nassert(spiro(n,d)\u003epi)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2017-08-08T14:35:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-06T18:54:26.000Z","updated_at":"2026-04-03T06:52:40.000Z","published_at":"2017-08-06T18:54:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumed that each bubble has practically the same diameter d. Given total number n of bubbles. Find volume v of breath.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2377,"title":"Area of a disk","description":"Find the area of a disk or circle. \r\n\r\nx= radius of the disk.","description_html":"\u003cp\u003eFind the area of a disk or circle.\u003c/p\u003e\u003cp\u003ex= radius of the disk.\u003c/p\u003e","function_template":"function y = crcl_area(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 12.57;\r\nassert(isequal(crcl_area(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 452.39;\r\nassert(abs(y_correct-crcl_area(x)) \u003c= 0.01)","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":377,"test_suite_updated_at":"2014-06-20T05:28:55.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2014-06-18T17:24:29.000Z","updated_at":"2026-04-30T06:34:22.000Z","published_at":"2014-06-18T17:25:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a disk or circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex= radius of the disk.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61306,"title":"Tire Slip Angle Calculation","description":"Slip angle represents the angle between the direction a tire is pointing and the direction it is moving.\r\nGiven Lateral velocity vy and Longitudinal velocity vx, compute slip angle α.\r\nEquation:\r\nalpha_angle = atan(vy / vx)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSlip angle represents the angle between the direction a tire is pointing and the direction it is moving.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Lateral velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evy \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLongitudinal velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evx, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecompute slip angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eα\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ealpha_angle = atan(vy / vx)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function alpha = slipAngle(vy,vx)\r\nalpha = vy;\r\nend","test_suite":"%%\r\nvy = 2; vx = 10;\r\nalpha_expected = 0.1974;\r\nassert(abs(slipAngle(vy,vx) - alpha_expected) \u003c 1e-4)\r\n\r\n%%\r\nvy = 1; vx = 5;\r\nalpha_expected = 0.1974;\r\nassert(abs(slipAngle(vy,vx) - alpha_expected) \u003c 1e-4)\r\n\r\n%%\r\nvy = 3; vx = 15;\r\nalpha_expected = 0.1974;\r\nassert(abs(slipAngle(vy,vx) - alpha_expected) \u003c 1e-4)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:23:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:23:12.000Z","updated_at":"2026-04-29T17:22:32.000Z","published_at":"2026-04-28T09:23:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSlip angle represents the angle between the direction a tire is pointing and the direction it is moving.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Lateral velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evy \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eLongitudinal velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evx, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ecompute slip angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eα\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ealpha_angle = atan(vy / vx)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":223,"title":"Which quadrant?","description":"Given a complex number, output quadrant 'I' 'II' 'III' or 'IV'\r\n\r\n        |              \r\n   II   |   I          \r\n        |              \r\n -------+------- real\r\n        |              \r\n   III  |   IV          \r\n        |\r\n      imag\r\n              \r\n","description_html":"\u003cp\u003eGiven a complex number, output quadrant 'I' 'II' 'III' or 'IV'\u003c/p\u003e\u003cpre\u003e        |              \r\n   II   |   I          \r\n        |              \r\n -------+------- real\r\n        |              \r\n   III  |   IV          \r\n        |\r\n      imag\u003c/pre\u003e","function_template":"function y = your_fcn_name(x)\r\n y='IV';\r\nend\r\nend","test_suite":"%%\r\nx = 1+1i;\r\ny_correct = 'I';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = -1-1i;\r\ny_correct = 'III';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1-1i;\r\ny_correct = 'IV';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = -1+1i;\r\ny_correct = 'II';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":368,"test_suite_updated_at":"2012-02-02T03:13:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-02T03:13:00.000Z","updated_at":"2026-04-27T23:04:05.000Z","published_at":"2012-02-02T03:13:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a complex number, output quadrant 'I' 'II' 'III' or 'IV'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[        |              \\n   II   |   I          \\n        |              \\n -------+------- real\\n        |              \\n   III  |   IV          \\n        |\\n      imag]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44618,"title":"surface areas of a cylinder","description":"There are 3 inputs: option, radius and height. If option= '1', compute the lateral surface area of the cylinder, for option 2 calculate the total surface area of the cylinder. For any other option, compute the total area of both flat sides of the cylinder.","description_html":"\u003cp\u003eThere are 3 inputs: option, radius and height. If option= '1', compute the lateral surface area of the cylinder, for option 2 calculate the total surface area of the cylinder. For any other option, compute the total area of both flat sides of the cylinder.\u003c/p\u003e","function_template":"function y = surface_area_cyl(optn,r,h)\r\n  y = r*h;\r\nend","test_suite":"%%\r\noptn=1;\r\nr=3;\r\nh=6;\r\ny_correct = 36*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=5;\r\nr=3;\r\nh=6;\r\ny_correct = 18*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=2;\r\nr=2;\r\nh=2;\r\ny_correct = 16*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=0;\r\nr=5;\r\nh=10;\r\ny_correct = 50*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=1;\r\nr=5;\r\nh=10;\r\ny_correct = 100*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=2;\r\nr=5;\r\nh=10;\r\ny_correct = 150*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=42;\r\nr=3;\r\nh=7;\r\ny_correct = 18*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=2;\r\nr=3\r\nh=7;\r\ny_correct = 60*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=1;\r\nr=3;\r\nh=7;\r\ny_correct = 42*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":53,"test_suite_updated_at":"2018-07-16T16:54:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-04-20T05:49:29.000Z","updated_at":"2026-04-03T06:59:13.000Z","published_at":"2018-04-20T05:49:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are 3 inputs: option, radius and height. If option= '1', compute the lateral surface area of the cylinder, for option 2 calculate the total surface area of the cylinder. For any other option, compute the total area of both flat sides of the cylinder.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45220,"title":"Find triangles from edge","description":"First input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\r\ne = [2, 4]\r\nand T a tetrahedron\r\nT = [1, 2, 3;...\r\n     1, 3, 4;...\r\n     1, 2, 4;...\r\n     2, 3, 4]\r\nthen the output of the function is\r\nS = [1, 2, 4;...\r\n     2, 3, 4]\r\nsince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\r\nConditions :\r\nIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\r\nEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\nOrder of rows / edges in the output doesn't matter.\r\nTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u003c t2 \u003c t3.\r\nEvery indices are positive, distinct integers.\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 286.1px; transform-origin: 408px 286.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.5px 8px; transform-origin: 374.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8.5px; tab-size: 4; transform-origin: 38.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2, 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.4583px 8px; transform-origin: 61.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand T a tetrahedron\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eT = [1, 2, 3;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e     1, 3, 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e     1, 2, 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.5667px 8px; transform-origin: 99.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output of the function is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 20.4333px; transform-origin: 405px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eS = [1, 2, 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.567px 8px; transform-origin: 197.567px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8167px 8px; transform-origin: 40.8167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConditions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 51.0833px; transform-origin: 392px 51.0833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 302.95px 8px; transform-origin: 302.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.6167px 8px; transform-origin: 69.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEdges are symmetric :\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 118.233px 8px; transform-origin: 118.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[e1, e2] is the same edge as [e2, e1]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 167.692px 8px; transform-origin: 167.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOrder of rows / edges in the output doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 330.342px 8px; transform-origin: 330.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 124.817px 8px; transform-origin: 124.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eindices are positive, distinct integers.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = find_triangles_from_edge(T,e)\r\n  S = [];\r\nend","test_suite":"%% Tetrahedron\r\nT = [1, 2, 3;...\r\n     1, 3, 4;...\r\n     1, 2, 4;...\r\n     2, 3, 4];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n     2, 3, 4];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Filled octahedron (two pyramids stuck together via their square bases)\r\nT = [1, 2, 3;...\r\n     1, 3, 4;...\r\n     1, 4, 5;...\r\n     1, 2, 5;...\r\n     2, 3, 6;...\r\n     3, 4, 6;...\r\n     4, 5, 6;...\r\n     2, 5, 6;...\r\n     2, 3, 4;...\r\n     2, 4, 5;...\r\n     1, 2, 4;...\r\n     2, 4, 6];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n     2, 3, 4;...\r\n     2, 4, 5;...\r\n     2, 4, 6];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Triangulated cube\r\nT = [1, 2, 4;...\r\n     2, 3, 4;...\r\n     5, 6, 8;...\r\n     6, 7, 8;...\r\n     1, 2, 5;...\r\n     2, 5, 6;...\r\n     2, 3, 6;...\r\n     3, 6, 7;...\r\n     3, 4, 7;...\r\n     4, 7, 8;...\r\n     1, 4, 8;...\r\n     1, 5, 8];\r\n\r\ne = [3, 7];\r\n\r\nS = [3, 4, 7;...\r\n     3, 6, 7];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Empty set test\r\nT = [2, 3, 5;...\r\n     3, 5, 7;...\r\n     5, 7, 11;...\r\n     7, 11, 13];\r\n\r\ne = [6, 8];\r\n\r\nassert(isempty(find_triangles_from_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_triangles_from_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2025-07-09T05:48:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-03T18:46:56.000Z","updated_at":"2026-04-17T18:45:00.000Z","published_at":"2019-12-03T20:30:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[e = [2, 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand T a tetrahedron\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [1, 2, 3;...\\n     1, 3, 4;...\\n     1, 2, 4;...\\n     2, 3, 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen the output of the function is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[S = [1, 2, 4;...\\n     2, 3, 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConditions :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEdges are symmetric :\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[e1, e2] is the same edge as [e2, e1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOrder of rows / edges in the output doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eindices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45358,"title":"Do they touch?","description":"The center and radius of two circles are given.\r\n\r\nDetermine whether they touch.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 25.5px; vertical-align: baseline; perspective-origin: 332px 25.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe center and radius of two circles are given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine whether they touch at one point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = touch(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx1=[0,0];\r\nx2=[5,5];\r\nr1=3;\r\nr2=2;\r\nassert(isequal(touch(x1,x2,r1,r2),0))\r\n\r\n%%\r\nx1=[0,0];\r\nx2=[3,4];\r\nr1=3;\r\nr2=2;\r\nassert(isequal(touch(x1,x2,r1,r2),1))\r\n\r\n%%\r\nx1=[2,1];\r\nx2=[3,4];\r\nr1=4;\r\nr2=2;\r\nassert(isequal(touch(x1,x2,r1,r2),0))\r\n\r\n%%\r\nx1=[-1,0];\r\nx2=[3,-3];\r\nr1=3;\r\nr2=8;\r\nassert(isequal(touch(x1,x2,r1,r2),1))\r\n\r\n%%\r\nx1=[-5,-5];\r\nx2=[5,5];\r\nr1=5;\r\nr2=5;\r\nassert(isequal(touch(x1,x2,r1,r2),0))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2020-02-26T14:39:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-26T14:25:46.000Z","updated_at":"2026-02-24T05:33:32.000Z","published_at":"2020-02-26T14:39:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center and radius of two circles are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine whether they touch at one point.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1141,"title":"Volume difference between Ellipsoid and Sphere ","description":"Given an ellipsoid of semi  principal axis (a,b,c) find the volume of the difference between this ellipsoid and  the sphere within, round the result toward zero using the \"floor\" function. ","description_html":"\u003cp\u003eGiven an ellipsoid of semi  principal axis (a,b,c) find the volume of the difference between this ellipsoid and  the sphere within, round the result toward zero using the \"floor\" function.\u003c/p\u003e","function_template":"function y = ellipsoid_sphere_diff(a,b,c)\r\n  y = x;\r\nend","test_suite":"%%\r\na=2;b=2;c=8;\r\ny_correct = 100;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n%%\r\na=4;b=4;c=4;\r\ny_correct =0;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n%%\r\na=3;b=5;c=8;\r\ny_correct= 389;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n%%\r\na=4;b=6;c=8;\r\ny_correct=536;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":5260,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":136,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":20,"created_at":"2012-12-25T23:34:50.000Z","updated_at":"2026-04-02T12:56:31.000Z","published_at":"2012-12-25T23:35:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an ellipsoid of semi principal axis (a,b,c) find the volume of the difference between this ellipsoid and the sphere within, round the result toward zero using the \\\"floor\\\" function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60166,"title":"Recursive triangle area","description":"Given triangle 1 with sides of length a, b, and c.  Triangle 2 is constructed within triangle 1 by bisecting each side.  Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides.  And so on. \r\nFind the area of triangle n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 71.9661px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 359.492px 35.9766px; transform-origin: 359.499px 35.9831px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 20.9896px; text-align: left; transform-origin: 336.497px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven triangle 1 with sides of length a, b, and c.  Triangle 2 is constructed within triangle 1 by bisecting each side.  Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides.  And so on. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 10.4948px; text-align: left; transform-origin: 336.497px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the area of triangle n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(a,b,c,n)\r\n  area = a+b+c+n;\r\nend","test_suite":"%%\r\na=1;b=1;c=sqrt(2);n=1;\r\ny_correct = 0.50;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=100;b=100;c=100;n=2;\r\ny_correct = 1082.53;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=13;b=33;c=44;n=4;\r\ny_correct = 2.0540;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3293343,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T18:08:43.000Z","updated_at":"2026-03-11T15:33:11.000Z","published_at":"2024-04-30T18:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven triangle 1 with sides of length a, b, and c.  Triangle 2 is constructed within triangle 1 by bisecting each side.  Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides.  And so on. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of triangle n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44282,"title":"Minimum possible M of the maximum side of a triangle of given area A.","description":"Suppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\r\n","description_html":"\u003cp\u003eSuppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\u003c/p\u003e","function_template":"function m = tri(a)\r\n  m = max(a/7);\r\nend","test_suite":"%%\r\na = 0.4331;\r\nm = 1.0001;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 43.31;\r\nm = 10.001;\r\nassert(tri(a)\u003cm*1.01)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003cm*1.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-10T11:39:30.000Z","updated_at":"2026-03-14T18:37:39.000Z","published_at":"2017-08-10T11:39:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose a triangle has area A. Suppose it has three sides S1, S2, and S3. Suppose M = max([S1 S2 S3]). What is the minimum possible value of M?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":49943,"title":"Splitting Hexagon - Problem the third","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 402px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 201px; transform-origin: 407px 201px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 279px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 139.5px; text-align: left; transform-origin: 384px 139.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the hexagon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 2 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5250;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[0 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[1 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3215;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.4981;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[4 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.8134;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 5 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5569;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T22:23:48.000Z","updated_at":"2025-12-27T03:32:18.000Z","published_at":"2021-01-22T22:24:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"273\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"307\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the 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Circle","description":"Consider a circle which has been divided into three concentric circles as depicted in the figure below\r\n\r\nThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 439.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 219.75px; transform-origin: 407px 219.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 315px 8px; transform-origin: 315px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 358.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.25px; text-align: left; transform-origin: 384px 179.25px; white-space: pre-wrap; margin-left: 4px; 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data-image-state=\"image-loaded\" width=\"359\" height=\"353\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = circle_split(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=circle_split(s);\r\ny_correct=[0.5774 0.8165];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[1 2 3];\r\ny=circle_split(s);\r\ny_correct=[0.4082 0.7071];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[3 2 1];\r\ny=circle_split(s);\r\ny_correct=[0.7071 0.9129];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[5 5 1];\r\ny=circle_split(s);\r\ny_correct=[0.6742 0.9535];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[4 4 0];\r\ny=circle_split(s);\r\ny_correct=[0.7071 1.0000];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":"2021-12-26T14:39:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T23:01:39.000Z","updated_at":"2026-04-28T12:38:25.000Z","published_at":"2021-01-22T23:03:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"353\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate 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of a spherical planet","description":"You just measured its surface area, that is the input.","description_html":"\u003cp\u003eYou just measured its surface area, that is the input.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 4*pi;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 400*pi;\r\ny_correct = 10;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 40000*pi;\r\ny_correct = 100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = -4*pi;\r\ny_correct = 1i;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":19,"comments_count":9,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4430,"test_suite_updated_at":"2012-02-15T16:29:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-27T21:02:01.000Z","updated_at":"2026-04-30T16:57:47.000Z","published_at":"2012-02-15T16:45:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou just measured its surface area, that is the input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45218,"title":"Find a common edge","description":"First input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie e1 \u003c e2 ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3 ;\r\n     1 3 4 ;\r\n     1 4 2 ;\r\n     2 3 4]\r\nand\r\ne = [2 3]\r\nthe output is the vector\r\nrow_idx = [1 4]\r\nsince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that edge [b a] is the same as edge [a b] so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 500.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 250.3px; transform-origin: 408px 250.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.083px 8px; transform-origin: 377.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.5417px 8px; transform-origin: 23.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ee1 \u0026lt; e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.358px 8px; transform-origin: 247.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eT = [1 2 3 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1 3 4 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1 4 2 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2 3 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 34.65px 8.5px; tab-size: 4; transform-origin: 34.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.667px 8px; transform-origin: 369.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.825px 8px; transform-origin: 117.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eedge [b a] is the same as edge [a b]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.725px 8px; transform-origin: 1.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_edge(T,e)\r\n  row_idx = e;\r\nend","test_suite":"%% Tetrahedron 1\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4];\r\n\r\ne = [2 3];\r\nrow_idx = [1 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Tetrahedron 2\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4];\r\n\r\ne = [2 4];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 5;...\r\n     1 5 2;...\r\n     6 3 2;...\r\n     6 4 3;...\r\n     6 5 4;...\r\n     6 2 5];\r\n\r\ne = [1 5];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n    2 3 4;...\r\n    5 6 8;...\r\n    6 7 8;...\r\n    1 2 5;...\r\n    2 5 6;...\r\n    2 3 6;...\r\n    3 6 7;...\r\n    3 4 7;...\r\n    4 7 8;...\r\n    4 1 8;...\r\n    1 8 5];\r\n\r\ne = [6 7];\r\nrow_idx = [4 8];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n     3 5 7;...\r\n     5 7 11;...\r\n     7 11 13];\r\n\r\ne = [6 28];\r\n\r\nassert(isempty(find_common_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2025-07-09T05:45:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T17:21:36.000Z","updated_at":"2026-04-17T18:42:43.000Z","published_at":"2019-12-01T18:01:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ee1 \u0026lt; e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if inputs are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [1 2 3 ;\\n     1 3 4 ;\\n     1 4 2 ;\\n     2 3 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[e = [2 3]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe output is the vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[row_idx = [1 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eedge [b a] is the same as edge [a b]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1443,"title":"Edges of a n-dimensional Hypercube","description":"Return the number of edges on an \u003chttp://en.wikipedia.org/wiki/Hypercube _n_-dimensional hypercube\u003e (with an integer n \u0026ge; 0).\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eReturn the number of edges on an \u003ca href = \"http://en.wikipedia.org/wiki/Hypercube\"\u003e\u003ci\u003en\u003c/i\u003e-dimensional hypercube\u003c/a\u003e (with an integer n \u0026ge; 0).\u003c/p\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function E = hypercube_edges(n)\r\n  E = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('hypercube_edges.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nE_correct = 0;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 1;\r\nE_correct = 1;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 2;\r\nE_correct = 4;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 3;\r\nE_correct = 12;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 4;\r\nE_correct = 32;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 5;\r\nE_correct = 80;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 6;\r\nE_correct = 192;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 7;\r\nE_correct = 448;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 8;\r\nE_correct = 1024;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 9;\r\nE_correct = 2304;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 10;\r\nE_correct = 5120;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 11;\r\nE_correct = 11264;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 12;\r\nE_correct = 24576;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 13;\r\nE_correct = 53248;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 14;\r\nE_correct = 114688;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 15;\r\nE_correct = 245760;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2013-04-28T07:06:47.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-04-22T11:46:41.000Z","updated_at":"2026-04-27T13:36:56.000Z","published_at":"2013-04-22T11:47:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the number of edges on an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Hypercube\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-dimensional hypercube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (with an integer n ≥ 0).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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Their robot’s arm reaches over a storage bin that is L inches long.  How long must the arm be to reach the object? Round to 1 decimal place.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA High School is trying to build their robot to be able to reach the hanging object which is H inches from the ground.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheir robot’s arm reaches over a storage bin that is L inches long.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHow long must the arm be to reach the object? 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Round to 2 decimal places.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 173px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 86.5px; transform-origin: 407px 86.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe total area of all four equal sections of the game field is N ft².\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEach section has a rectangle of dimensions X ft x Y ft reserved for a hanging scoring rack.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere is also a scoring bin that takes up an area of 1ft x 1ft.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHow much driving area does the robot have in each section? Round to 2 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 101px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 50.5px; text-align: left; transform-origin: 384px 50.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = findArea(N,X,Y) % Do not edit this line.\r\n  % insert your code here\r\n  N = ?;\r\nend % Do not edit this line.\r\n\r\n","test_suite":"%%\r\nassert(isequal(findArea(576, 2, 2),139));\r\n%%\r\nassert(isequal(findArea(333, 4, 4),66.25));\r\n%%\r\nassert(isequal(findArea(128.5, 4, 4),15.13));","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":542228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":323,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T16:30:44.000Z","updated_at":"2026-04-30T21:23:21.000Z","published_at":"2022-09-13T16:30:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total area of all four equal sections of the game field is N ft².\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eEach section has a rectangle of dimensions X ft x Y ft reserved for a hanging scoring rack.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThere is also a scoring bin that takes up an area of 1ft x 1ft.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHow much driving area does the robot have in each section? Round to 2 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"95\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"145\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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a sequence of points forming a closed path (first and last points are coincident) return the perimeter value.\r\nFor example:\r\n\r\n xy = [ 0,0 ;\r\n        1,0 ;\r\n        1,1 ;\r\n        0,1 ;\r\n        0,0 ];\r\n\r\n L = 4","description_html":"\u003cp\u003eGiven a sequence of points forming a closed path (first and last points are coincident) return the perimeter value.\r\nFor example:\u003c/p\u003e\u003cpre\u003e xy = [ 0,0 ;\r\n        1,0 ;\r\n        1,1 ;\r\n        0,1 ;\r\n        0,0 ];\u003c/pre\u003e\u003cpre\u003e L = 4\u003c/pre\u003e","function_template":"function L = perimeter1(xy)\r\n\r\n  L=xy;\r\n\r\nend","test_suite":"%% Test case 1: Square\r\n\r\nxy=[0,0;\r\n    1,0;\r\n    1,1;\r\n    0,1;\r\n    0,0];\r\n\r\n\r\nerr=(abs(perimeter1(xy)-4)/(4))*100;\r\nassert(err\u003c.1)\r\n\r\n%% Test case 2 : Circle\r\n\r\nt=[0:pi/100:2*pi,0]';\r\nxy=[cos(t),sin(t)];\r\n\r\n\r\nerr=(abs(perimeter1(xy)-2*pi)/(2*pi))*100;\r\nassert(err\u003c.1)\r\n\r\n%% Test case 4 : Half-circle\r\n\r\nt=[0:pi/100:pi,0]';\r\nxy=[cos(t),sin(t)];\r\n\r\nerr=(abs(perimeter1(xy)-(pi+2))/(2+pi))*100;\r\nassert(err\u003c.1)\r\n\r\n%% Test case 4 : Hexagon\r\n\r\nside=rand;\r\nx=side*[-1 -0.5 0.5 1 0.5 -0.5 -1];\r\ny=side*sqrt(3)*[0 -0.5 -0.5 0 0.5 0.5 0];\r\nxy=[x',y'];\r\nerr=(abs(perimeter1(xy)-(6*side))/(6*side))*100;\r\nassert(err\u003c.1)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":10742,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":157,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":20,"created_at":"2013-03-25T10:56:31.000Z","updated_at":"2026-04-07T18:48:49.000Z","published_at":"2013-03-25T10:57:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sequence of points forming a closed path (first and last points are coincident) return the perimeter value. For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ xy = [ 0,0 ;\\n        1,0 ;\\n        1,1 ;\\n        0,1 ;\\n        0,0 ];\\n\\n L = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":132,"title":"given 3 sides, find area of this triangle","description":"1:3 -\u003e 0; 3:5 -\u003e 6 ","description_html":"\u003cp\u003e1:3 -\u003e 0; 3:5 -\u003e 6\u003c/p\u003e","function_template":"function y = your_fcn_name(a,b,c)\r\n  y = x;\r\nend","test_suite":"%%\r\na=1; b=2; c=3;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(a,b,c),y_correct))\r\n%%\r\na=3; b=4; c=5;\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(a,b,c),y_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":821,"test_suite_updated_at":"2012-01-28T04:51:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-28T04:51:58.000Z","updated_at":"2026-04-23T21:15:08.000Z","published_at":"2012-01-28T06:11:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1:3 -\u003e 0; 3:5 -\u003e 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60980,"title":"Mesh the tetrahedron","description":"Problem statement\r\n\r\nAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n       \r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0 and Y \u003e 0) here can be [1, 2, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.592px 8px; transform-origin: 374.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 328.017px 8px; transform-origin: 328.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.51667px 8px; transform-origin: 7.51667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.4667px 8px; transform-origin: 49.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.5917px 8px; transform-origin: 13.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.2917px 8px; transform-origin: 53.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_tetrahedron()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 4;\r\n             2 3 4;\r\n             3 1 4;\r\n             1 3 2];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_tetrahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_tetrahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:43:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2025-07-23T16:17:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T11:03:01.000Z","updated_at":"2026-04-21T19:49:47.000Z","published_at":"2025-07-23T11:11:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Segment Area","description":"Let us consider a circle with radius . If we draw an angle  (in radians) from the center of the circle, the two radii forming that angle intersect the circle at  and . We call  the area delimited by the chord and the arc  (the so-called Circular Segment, blu in the figure). \r\n\r\nFor a given radius  and area , compute the angle  (rounded to 6 significant digits).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 276.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 138.31px; transform-origin: 406.996px 138.31px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 62.7273px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 31.3636px; text-align: left; transform-origin: 383.999px 31.3636px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLet us consider a circle with radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35.5\" height=\"17.5\" style=\"width: 35.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If we draw an angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59.5\" height=\"17.5\" style=\"width: 59.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (in radians) from the center of the circle, the two radii forming that angle intersect the circle at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. We call \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"17.5\" style=\"width: 36.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the area delimited by the chord and the arc \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23\" height=\"17.5\" style=\"width: 23px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (the so-called Circular Segment, blu in the figure). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 175px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 87.5px; text-align: left; transform-origin: 383.999px 87.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"161\" height=\"175\" style=\"vertical-align: middle;width: 161px;height: 175px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9091px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4545px; text-align: left; transform-origin: 383.999px 10.4545px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, compute the angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (rounded to 6 significant digits).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = area_segment(r,a)\r\n  t=;\r\nend","test_suite":"%%\r\nr = 1;\r\na = pi/2;\r\nt_correct = pi;\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n\r\n%%\r\nr = 1;\r\na = pi/4-1/2;\r\nt_correct = pi/2;\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n\r\n%%\r\nr = 2;\r\na = 4;\r\nt_correct = 2.55419595;\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n\r\n%%\r\nr = sqrt(2);\r\nt_correct = pi*rand();\r\na = t_correct-sin(t_correct);\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-22T13:20:31.000Z","updated_at":"2026-04-14T12:49:23.000Z","published_at":"2021-08-22T13:32:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet us consider a circle with radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If we draw an angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et \\\\in [0,\\\\pi]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (in radians) from the center of the circle, the two radii forming that angle intersect the circle at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. We call \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\\\\ge0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the area delimited by the chord and the arc \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (the so-called Circular Segment, blu in the figure). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"175\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"161\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (rounded to 6 significant digits).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":61310,"title":"Electric Power Steering (EPS) Assist Curve Calculation","description":"Electric Power Steering (EPS) provides assist torque proportional to driver input.\r\nGiven Steering torque Ts and Gain k, Compute assist torque Ta.\r\nEquation:\r\nTa = k × Ts","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eElectric Power Steering (EPS) provides assist torque proportional to driver input.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Steering torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTs \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGain \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute assist torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTa\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTa = k × Ts\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Ta = epsAssist(Ts,k)\r\nTa =0;\r\nend","test_suite":"%%\r\nTs = 4; \r\nk = 3;\r\nTa_expected = 12;\r\nassert(isequal(epsAssist(Ts,k),Ta_expected))\r\n\r\n%%\r\nTs = 5; \r\nk = 2;\r\nTa_expected = 10;\r\nassert(isequal(epsAssist(Ts,k),Ta_expected))\r\n\r\n%%\r\nTs = 6; \r\nk = 1.5;\r\nTa_expected = 9;\r\nassert(isequal(epsAssist(Ts,k),Ta_expected))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:39:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:39:20.000Z","updated_at":"2026-04-29T17:30:10.000Z","published_at":"2026-04-28T09:39:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eElectric Power Steering (EPS) provides assist torque proportional to driver input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Steering torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTs \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eGain \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute assist torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTa\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTa = k × Ts\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61307,"title":"Steering Ratio Calculation","description":"The steering ratio defines the relationship between steering wheel angle and road wheel angle.\r\nGiven wheel angle δ and Steering ratio N, Compute steering wheel angle swa.\r\nEquation:\r\nswa = N × delta","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe steering ratio defines the relationship between steering wheel angle and road wheel angle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδ \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand Steering ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eN, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute steering wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eswa\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eswa = N × delta\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function sw = steeringWheelAngle(delta,N)\r\nsw = N;\r\nend","test_suite":"%%\r\ndelta = 5*pi/180; \r\nN = 16;\r\nsw_expected = 1.3963;\r\nassert(abs(steeringWheelAngle(delta,N) - sw_expected) \u003c 1e-4)\r\n\r\n%%\r\ndelta = 3*pi/180; \r\nN = 18;\r\nsw_expected = 0.9425;\r\nassert(abs(steeringWheelAngle(delta,N) - sw_expected) \u003c 1e-4)\r\n\r\n%%\r\ndelta = 10*pi/180; \r\nN = 14;\r\nsw_expected = 2.4435;\r\nassert(abs(steeringWheelAngle(delta,N) - sw_expected) \u003c 1e-4)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:26:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:26:22.000Z","updated_at":"2026-04-29T17:24:14.000Z","published_at":"2026-04-28T09:26:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe steering ratio defines the relationship between steering wheel angle and road wheel angle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδ \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand Steering ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute steering wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eswa\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eswa = N × delta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61309,"title":"Steering Torque Estimation","description":"Steering torque is generated due to lateral tire forces acting through the steering mechanism.\r\nGiven Lateral force Fy and Lever arm r, Compute torque T.\r\nEquation:\r\nT = Fy × r","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteering torque is generated due to lateral tire forces acting through the steering mechanism.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Lateral force \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFy \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLever arm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eT = Fy × r\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = steeringTorque(Fy,r)\r\nT = 0;\r\nend","test_suite":"%%\r\nFy = 1500; \r\nr = 0.15;\r\nT_expected = 225;\r\nassert(isequal(steeringTorque(Fy,r),T_expected))\r\n\r\n%%\r\nFy = 1000; \r\nr = 0.2;\r\nT_expected = 200;\r\nassert(isequal(steeringTorque(Fy,r),T_expected))\r\n\r\n%%\r\nFy = 800; \r\nr = 0.25;\r\nT_expected = 200;\r\nassert(isequal(steeringTorque(Fy,r),T_expected))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:36:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:36:45.000Z","updated_at":"2026-04-30T06:50:23.000Z","published_at":"2026-04-28T09:36:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSteering torque is generated due to lateral tire forces acting through the steering mechanism.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Lateral force \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFy \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eLever arm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eT = Fy × r\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61308,"title":"Understeer or Oversteer Gradient Calculation","description":"This gradient determines whether a vehicle tends to understeer or oversteer.\r\nGiven Mass m, Wheelbase L, Front cornering stiffness Cf and Rear cornering stiffness Cr, Compute understeer/oversteer gradient K.\r\nEquation:\r\nK = (m / L) × ( (1 / Cf) − (1 / Cr) )","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis gradient determines whether a vehicle tends to understeer or oversteer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003em, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFront cornering stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRear cornering stiffness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCr, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute understeer/oversteer gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eK\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eK = (m / L) × ( (1 / Cf) − (1 / Cr) )\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function K = understeerGradient(m,L,Cf,Cr)\r\nK = Cr;\r\nend","test_suite":"%%\r\nm = 1500; \r\nL = 2.7; \r\nCf = 80000; \r\nCr = 90000;\r\nK_expected = 0.001543;\r\nassert(abs(understeerGradient(m,L,Cf,Cr) - K_expected) \u003c 1e-3)\r\n\r\n%%\r\nm = 1200; \r\nL = 2.5; \r\nCf = 70000; \r\nCr = 85000;\r\nK_expected = 0.001029;\r\nassert(abs(understeerGradient(m,L,Cf,Cr) - K_expected) \u003c 1e-3)\r\n\r\n%%\r\nm = 1800; \r\nL = 3.0; \r\nCf = 90000; \r\nCr = 95000;\r\nK_expected = 0.000351;\r\nassert(abs(understeerGradient(m,L,Cf,Cr) - K_expected) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:34:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:31:51.000Z","updated_at":"2026-04-30T16:28:44.000Z","published_at":"2026-04-28T09:34:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis gradient determines whether a vehicle tends to understeer or oversteer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eWheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFront cornering stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eRear cornering stiffness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCr, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute understeer/oversteer gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = (m / L) × ( (1 / Cf) − (1 / Cr) )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61304,"title":"Turning radius of a vehicle","description":"The turning radius represents the radius of the circular path followed by a vehicle.\r\nGiven Wheelbase L and Steering angle δ, Compute the turning radius R.\r\nEquation:\r\nR = L / tan(delta)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Wheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteering angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδ, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the turning radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eR = L / tan(delta)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function R = turningRadius(L,delta)\r\nR = 0;\r\nend","test_suite":"%%\r\nL = 2.5; delta = 30*pi/180;\r\nR_expected = 4.3301;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 3.0; delta = 20*pi/180;\r\nR_expected = 8.2426;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 2.8; delta = 10*pi/180;\r\nR_expected = 15.866;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-1)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:16:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:13:54.000Z","updated_at":"2026-04-30T16:29:38.000Z","published_at":"2026-04-28T09:16:45.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Wheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSteering angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδ, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the turning radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = L / tan(delta)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61305,"title":"Yaw rate of the vehicle","description":"Yaw rate defines how quickly a vehicle rotates about its vertical axis during motion.\r\nGiven Vehicle speed v and Turning radius R, compute yaw rate r.\r\nEquation:\r\nr = v / R","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYaw rate defines how quickly a vehicle rotates about its vertical axis during motion.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Vehicle speed \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ev \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTurning radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eR, c\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eompute yaw rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er = v / R\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = yawRate(v,R)\r\nr = v;\r\nend","test_suite":"%%\r\nv = 15; R = 30;\r\nr_expected = 0.5;\r\nassert(abs(yawRate(v,R) - r_expected) \u003c 1e-6)\r\n\r\n%%\r\nv = 20; R = 40;\r\nr_expected = 0.5;\r\nassert(abs(yawRate(v,R) - r_expected) \u003c 1e-6)\r\n\r\n%%\r\nv = 10; R = 25;\r\nr_expected = 0.4;\r\nassert(abs(yawRate(v,R) - r_expected) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:18:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:18:24.000Z","updated_at":"2026-05-01T02:44:50.000Z","published_at":"2026-04-28T09:18:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYaw rate defines how quickly a vehicle rotates about its vertical axis during motion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Vehicle speed \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eTurning radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR, c\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eompute yaw rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er = v / R\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58743,"title":"Find the surface area of a cone.","description":"For instance,\r\nGiven r (radius) = 3, and s (slant height) = 5:\r\nsurface area should be 94.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 40.5px; transform-origin: 407.5px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor instance,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven r (radius) = 3, and s (slant height) = 5:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esurface area should be 94.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = findArea(r,s)\r\n  y = x;\r\nend","test_suite":"%%\r\nr = 3;\r\ns = 5;\r\ny_correct = 75;\r\nassert(isequal(findArea(r,s),y_correct))\r\n\r\n%%\r\nr = 1;\r\ns = 4;\r\ny_correct = 16;\r\nassert(isequal(findArea(r,s),y_correct))\r\n\r\n%%\r\nr = 2;\r\ns = 8;\r\ny_correct = 63;\r\nassert(isequal(findArea(r,s),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3470333,"edited_by":3470333,"edited_at":"2023-07-18T20:23:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2023-07-18T20:23:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-18T20:21:34.000Z","updated_at":"2026-04-29T19:33:29.000Z","published_at":"2023-07-18T20:23:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor instance,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven r (radius) = 3, and s (slant height) = 5:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esurface area should be 94.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48015,"title":"Calculate the volume of the football","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63.9631px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 31.9744px; transform-origin: 406.996px 31.9815px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9091px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4545px; text-align: left; transform-origin: 383.999px 10.4545px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate the volume of a football given the ball radius r, using the formula below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.0625px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 17.0312px; text-align: left; transform-origin: 383.999px 17.0312px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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width=\"88\" height=\"34\" style=\"width: 88px; height: 34px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = calcVolume(r)\r\n\r\n    y = r;\r\nend","test_suite":"%%\r\nr = 2;\r\ny_correct = 33.5103;\r\nassert(abs(calcVolume(r) - y_correct) \u003c 0.1)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":808745,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T14:17:48.000Z","updated_at":"2026-04-05T10:34:30.000Z","published_at":"2020-12-17T14:17:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the volume of a football given the ball radius r, using the formula below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV_{sphere} = \\\\frac43 \\\\pi r^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44880,"title":"Angle between two vectors","description":"Given 2 pairs of _cartesian co-ordinates_, determine the angle between the 2 vectors formed by the _points_ and the _origin_. Angle must be in [0,180] and in degrees.\r\n\r\ne.g. \r\n\r\n* Input (3 separate inputs)\r\n\r\n  [0 1;2 0]\r\n  [1 1;-2 0]\r\n  [1 1;2 2]\r\n\r\n* Output (3 separate outputs):\r\n\r\n  90\r\n  135\r\n  0","description_html":"\u003cp\u003eGiven 2 pairs of \u003ci\u003ecartesian co-ordinates\u003c/i\u003e, determine the angle between the 2 vectors formed by the \u003ci\u003epoints\u003c/i\u003e and the \u003ci\u003eorigin\u003c/i\u003e. Angle must be in [0,180] and in degrees.\u003c/p\u003e\u003cp\u003ee.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003eInput (3 separate inputs)\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e[0 1;2 0]\r\n[1 1;-2 0]\r\n[1 1;2 2]\r\n\u003c/pre\u003e\u003cul\u003e\u003cli\u003eOutput (3 separate outputs):\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e90\r\n135\r\n0\r\n\u003c/pre\u003e","function_template":"function y = angle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 1;-1 -1];\r\ny_correct = 180;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;-1 -1];\r\ny_correct = 90;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0.5 sqrt(3)/2;0.2 0];\r\ny_correct = 60;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;0.5 sqrt(3)/2];\r\ny_correct = 75;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0 1;0 5];\r\ny_correct = 0;\r\nassert(isequal(angle(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":290843,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-02T11:16:36.000Z","updated_at":"2026-02-28T08:22:03.000Z","published_at":"2019-04-02T11:17:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven 2 pairs of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecartesian co-ordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, determine the angle between the 2 vectors formed by the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epoints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eorigin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Angle must be in [0,180] and in degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput (3 separate inputs)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[0 1;2 0]\\n[1 1;-2 0]\\n[1 1;2 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput (3 separate outputs):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[90\\n135\\n0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42686,"title":"What's the missing interior angle?","description":"I'm talking about polygons...  The sum of the interior angles of a triangle is 180 degrees.  The sum of the interior angles of a quadrilateral is 360 degrees, and so on.\r\n\r\nFor this problem, you are given n-1 angles (in degrees) of an n-sided polygon.  Please return the final angle.\r\n\r\nTriangle examples:\r\n\r\n  \u003e\u003ea=missing_interior_angle([60 60])\r\n  a =\r\n      60\r\n  \u003e\u003ea=missing_interior_angle([45 45])\r\n  a =\r\n      90","description_html":"\u003cp\u003eI'm talking about polygons...  The sum of the interior angles of a triangle is 180 degrees.  The sum of the interior angles of a quadrilateral is 360 degrees, and so on.\u003c/p\u003e\u003cp\u003eFor this problem, you are given n-1 angles (in degrees) of an n-sided polygon.  Please return the final angle.\u003c/p\u003e\u003cp\u003eTriangle examples:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt;a=missing_interior_angle([60 60])\r\na =\r\n    60\r\n\u0026gt;\u0026gt;a=missing_interior_angle([45 45])\r\na =\r\n    90\r\n\u003c/pre\u003e","function_template":"function y = missing_interior_angle(x)\r\n  y = 180 - sum(x);\r\nend","test_suite":"%%\r\nx = [60 60];\r\ny_correct = 60;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = [45 90];\r\ny_correct = 45;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = [90 70 70];\r\ny_correct = 130;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = [120 120 120 110 110];\r\ny_correct = 140;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n%%\r\nx = 140*ones(1,8);\r\ny_correct = 140;\r\nassert(isequal(missing_interior_angle(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":57863,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":92,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-11-16T01:39:37.000Z","updated_at":"2026-02-10T11:40:46.000Z","published_at":"2015-11-16T01:40:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI'm talking about polygons... The sum of the interior angles of a triangle is 180 degrees. The sum of the interior angles of a quadrilateral is 360 degrees, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you are given n-1 angles (in degrees) of an n-sided polygon. Please return the final angle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangle examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003ea=missing_interior_angle([60 60])\\na =\\n    60\\n\u003e\u003ea=missing_interior_angle([45 45])\\na =\\n    90]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46063,"title":"Area of a pentagon","description":"Given the side of a regular pentagon and its apothem return the area of pentagon.\r\n\r\nRemember the area of pentagon is calculate as the product between perimeter and the apothem divided by 2. ","description_html":"\u003cp\u003eGiven the side of a regular pentagon and its apothem return the area of pentagon.\u003c/p\u003e\u003cp\u003eRemember the area of pentagon is calculate as the product between perimeter and the apothem divided by 2.\u003c/p\u003e","function_template":"function area = pentagon_Area(s,A)\r\n  area=s^2;\r\nend","test_suite":"%%\r\ns = 8;\r\nA = 9;\r\narea_correct = 180;\r\nassert(isequal(pentagon_Area(s,A),area_correct))\r\n\r\n%%\r\ns=pi;\r\nA=9;\r\narea_correct=(45/2)*pi;\r\nassert(isequal(pentagon_Area(s,A),area_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":426918,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":85,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-07-27T22:20:36.000Z","updated_at":"2026-04-13T13:29:19.000Z","published_at":"2020-07-27T22:21:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the side of a regular pentagon and its apothem return the area of pentagon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemember the area of pentagon is calculate as the product between perimeter and the apothem divided by 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45468,"title":"Determine the perimeter of a three-quarter circle","description":"If a circle has a diameter of x as an input value, then show the value of the perimeter of the three-quarter circle in output variable y. Remember that, you must show the output value of the perimeter, y to 15 decimal place.  \r\n","description_html":"\u003cp\u003eIf a circle has a diameter of x as an input value, then show the value of the perimeter of the three-quarter circle in output variable y. Remember that, you must show the output value of the perimeter, y to 15 decimal place.\u003c/p\u003e","function_template":"function y = circle_diameter(x)\r\ny = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 6.712388980384690;\r\nassert(isequal(circle_diameter(x),y_correct))\r\n\r\n%%\r\nx = 5.5;\r\ny_correct = 18.459069696057895;\r\nassert(isequal(circle_diameter(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":430818,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":"2020-04-26T21:34:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-19T16:22:42.000Z","updated_at":"2026-02-16T12:04:56.000Z","published_at":"2020-04-19T17:29:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a circle has a diameter of x as an input value, then show the value of the perimeter of the three-quarter circle in output variable y. Remember that, you must show the output value of the perimeter, y to 15 decimal place.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45488,"title":"Height of a 3D Pyramid ","description":"If a pyramid is made with one(1). What will be the height of the pyramid of square shaped base(n*n)? where input is n.","description_html":"\u003cp\u003eIf a pyramid is made with one(1). What will be the height of the pyramid of square shaped base(n*n)? where input is n.\u003c/p\u003e","function_template":"function h = pyramid(n)\r\n  h = n;\r\nend","test_suite":"%%\r\nn = 10;\r\ny_correct = 5;\r\nassert(isequal(pyramid(n),y_correct))\r\n%%\r\nn = 19;\r\ny_correct = 10;\r\nassert(isequal(pyramid(n),y_correct))\r\n%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(pyramid(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":432893,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2020-04-30T19:41:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-30T19:37:13.000Z","updated_at":"2026-02-11T12:11:39.000Z","published_at":"2020-04-30T19:37:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a pyramid is made with one(1). What will be the height of the pyramid of square shaped base(n*n)? where input is n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45333,"title":"Area-01","description":"Given the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\r\n\r\n","description_html":"\u003cp\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/p\u003e","function_template":"function y = inscribed_circle(r)\r\n  y = x;\r\nend","test_suite":"%%\r\nr = 1;\r\ny_correct = 0.8584;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 5;\r\ny_correct = 21.4602;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 0;\r\ny_correct = 0;\r\nassert(isequal(inscribed_circle(r),y_correct))\r\n%%\r\nr = 12.1;\r\ny_correct = 125.6794;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-16T18:24:27.000Z","updated_at":"2026-02-09T14:23:49.000Z","published_at":"2020-02-16T18:24:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2999,"title":"Billiards","description":"Considering there are 15 pool balls, (b), in the game of pool, and given a radius, (r). What is the volume, (V), of a rack in the game of pool?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381px 8px; transform-origin: 381px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsidering there are 15 pool balls, (b), in the game of pool, and given a radius, (r). What is the volume, (V), of a rack in the game of pool?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Volume_Rack(x)\r\nend","test_suite":"\r\n%%\r\nx = 2.438;\r\ny_correct = 910.502;\r\ny_calc = Volume_Rack(x);\r\nassert(abs((y_correct - y_calc) / y_correct) \u003c 1e-4)\r\n\r\n%%\r\nx = 2.25;\r\ny_correct = 715.694;\r\ny_calc = Volume_Rack(x);\r\nassert(abs((y_correct - y_calc) / y_correct) \u003c 1e-4)\r\n\r\n%%\r\nx = 2;\r\ny_correct = 502.659;\r\ny_calc = Volume_Rack(x);\r\nassert(abs((y_correct - y_calc) / y_correct) \u003c 1e-4)","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":34016,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2021-11-02T04:54:44.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-02-11T01:06:55.000Z","updated_at":"2026-02-17T09:08:22.000Z","published_at":"2015-02-11T01:30:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsidering there are 15 pool balls, (b), in the game of pool, and given a radius, (r). What is the volume, (V), of a rack in the game of pool?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44240,"title":"Area of a Square","description":"Given the length x of the side of a regular square, find the area of the square, A.","description_html":"\u003cp\u003eGiven the length x of the side of a regular square, find the area of the square, A.\u003c/p\u003e","function_template":"function A = sq_area(x)\r\n  A = x;\r\nend","test_suite":"%%\r\nx = 1;\r\nA = 1;\r\nassert(isequal(sq_area(x),A))\r\n\r\n%%\r\nx = 2;\r\nA = 4;\r\nassert(isequal(sq_area(x),A))\r\n\r\n%%\r\nx = 6;\r\nA = 36;\r\nassert(isequal(sq_area(x),A))\r\n\r\n%%\r\nx = 8;\r\nA = 64;\r\nassert(isequal(sq_area(x),A))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":138544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":733,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-06-20T20:38:32.000Z","updated_at":"2026-04-23T00:00:49.000Z","published_at":"2017-06-21T15:37:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the length x of the side of a regular square, find the area of the square, A.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45217,"title":"Find a common vertex","description":"First input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4]\r\nand\r\ni = 2\r\nthe output is the vector\r\nrow_idx = [1 3 4]\r\nsince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 479.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 239.8px; transform-origin: 408px 239.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.725px 8px; transform-origin: 375.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003eT = [1 2 3;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e     1 3 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 8.5px; transform-origin: 42.35px 8.5px; \"\u003e     1 4 2;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2 3 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ei = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 3 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.533px 8px; transform-origin: 367.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_vertex(T,i)\r\n  row_idx = i;\r\nend","test_suite":"%% Tetrahedron\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4];\r\n\r\ni = 2;\r\n\r\nrow_idx = [1 3 4];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 5;...\r\n     1 5 2;...\r\n     6 3 2;...\r\n     6 4 3;...\r\n     6 5 4;...\r\n     6 2 5];\r\n\r\ni = 4;\r\n\r\nrow_idx = [2 3 6 7];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n     2 3 4;...\r\n     5 6 8;...\r\n     6 7 8;...\r\n     1 2 5;...\r\n     2 5 6;...\r\n     2 3 6;...\r\n     3 6 7;...\r\n     3 4 7;...\r\n     4 7 8;...\r\n     4 1 8;...\r\n     1 8 5];\r\n\r\ni = 6;\r\n\r\nrow_idx = [3 4 6 7 8];\r\n\r\nassert(isequal(find_common_vertex(T,i),row_idx) || isequal(find_common_vertex(T,i),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n     3 5 7;...\r\n     5 7 11;...\r\n     7 11 13];\r\n\r\ni = 8;\r\n\r\nassert(isempty(find_common_vertex(T,i)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_vertex.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2025-07-09T05:47:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T16:22:33.000Z","updated_at":"2026-04-17T18:43:23.000Z","published_at":"2019-12-01T16:58:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst input is T, a triplet list of indices. Second input is i, a single index (positive integer). The goal of this function is to find and return the indices of the rows in the list which contain this particular index. Output format is indifferently a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if inputs are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [1 2 3;...\\n     1 3 4;...\\n     1 4 2;...\\n     2 3 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[i = 2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe output is the vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[row_idx = [1 3 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince 2 is contained in rows number 1, 3, and 4 of T. If the index is not in the list, the function must of course return the empty set. Each index is at most contained once per row / triplet.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2465,"title":"Find the area of a rectangle if length of the diagonal is given.","description":"if length of a diagnonal in rectangle is 5. Its area is 12.","description_html":"\u003cp\u003eif length of a diagnonal in rectangle is 5. Its area is 12.\u003c/p\u003e","function_template":"function y = area_rect(x)\r\n  y = ;\r\nend","test_suite":"%%\r\nx=5;\r\ny_correct = 12;\r\nassert(isequal(area_rect(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":28146,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":169,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-25T13:24:47.000Z","updated_at":"2026-02-18T10:51:56.000Z","published_at":"2014-07-25T13:26:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif length of a diagnonal in rectangle is 5. Its area is 12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60576,"title":"Perimeter of a Koch snowflake","description":"A Koch snowflake is an iteratively generated (fractal) shape built out of successively smaller equilateral triangles by following these steps: \r\nDraw an equilateral triangle. (n = 0)\r\nDivide the line segment into three segments of equal length.\r\nDraw an equilateral triangle that has the middle segment from step 2 as its base and points outward.\r\nremove the line segment that is the base of the triangle from step 3. (n = 1) \r\nRepeat steps 2 - 4. (n = 2,3,...) \r\nIn the limit of  this shape has an infinite perimeter and a finite area. For , this perimeter is calculable. Calculate both of these values for any input value of n and any starting triangle edge length, s.\r\n[A1,P1] = KochSnowflake(n,s)\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 554.062px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 277.025px; transform-origin: 332px 277.031px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 21px; text-align: left; transform-origin: 309px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Koch snowflake is an iteratively generated (fractal) shape built out of successively smaller equilateral triangles by following these steps: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 122.625px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 316px 61.3125px; transform-origin: 316px 61.3125px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDraw an equilateral triangle. (n = 0)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDivide the line segment into three segments of equal length.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 20.4375px; text-align: left; transform-origin: 288px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDraw an equilateral triangle that has the middle segment from step 2 as its base and points outward.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eremove the line segment that is the base of the triangle from step 3. (n = 1) \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288px 10.2125px; text-align: left; transform-origin: 288px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRepeat steps 2 - 4. (n = 2,3,...) \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the limit of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e this shape has an infinite perimeter and a finite area. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"43\" height=\"18\" style=\"width: 43px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, this perimeter is calculable. Calculate both of these values for any input value of n and any starting triangle edge length, s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 329px 10.2125px; transform-origin: 329px 10.2188px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[A1,P1] = KochSnowflake(n,s)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 256px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 309px 128px; text-align: left; transform-origin: 309px 128px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"256\" height=\"256\" style=\"vertical-align: middle;width: 256px;height: 256px\" src=\"data:image/png;base64,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\" alt=\"n = 0,1,2,3 of Koch Snowflake\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Area,Perimeter] = KochSnowflake(n,s)\r\n  Area = [];\r\n  Perimeter =[];\r\nend","test_suite":"filetext = fileread('KochSnowflake.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'eval') || ...\r\n          contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\nassert(~illegal)\r\n%% \r\nn=1;s=sqrt(5);\r\nA_correct=5.773502691896258/2;\r\nP_correct=8.944271909999159;\r\n[A,P]=KochSnowflake(n,s);\r\n[A,A_correct]\r\nassert(all(abs([A,P]-[A_correct,P_correct])\u003c1E-12));\r\n%% \r\nn=2;s=sqrt(7);\r\nA_correct=8.981004187394181/2;\r\nP_correct=14.110673659011150;\r\n[A,P]=KochSnowflake(n,s);\r\n[A,A_correct]\r\nassert(all(abs([A,P]-[A_correct,P_correct])\u003c1E-12));\r\n%% \r\nn=20;s=sqrt(9);\r\nA_correct=12.470765391560523/2;\r\nP_correct=2838.031696810952;\r\n[A,P]=KochSnowflake(n,s);\r\n[A,A_correct]\r\nassert(all(abs([A,P]-[A_correct,P_correct])\u003c1E-12));\r\n%%\r\nn = 0;s=1:20;\r\nP_correct = 3*s;\r\nA_correct = s.^2*sqrt(3)/4;\r\nfor i = 1:20\r\n    [A,P]=KochSnowflake(n,s(i));\r\n    assert(all(abs([A,P]-[A_correct(i),P_correct(i)])\u003c1E-12));\r\nend\r\n%%\r\nn=1:20;s=1.5;\r\nP_correct = (9*(4/3).^n)/2;\r\nA_correct = 9*sqrt(3)*(8-3*(4/9).^n)/80;\r\nfor i = 1:20\r\n    [A,P]=KochSnowflake(n(i),s);\r\n    assert(all(abs([A,P]-[A_correct(i),P_correct(i)])\u003c1E-12));\r\nend\r\n%% \r\nn = 12345678900000000000;s=987654321000;\r\nP_correct = Inf;\r\nA_correct = 1.35163849E24/2;\r\n[A,P]=KochSnowflake(n,s);\r\nassert(abs(A-A_correct)\u003c1E15\u0026isinf(P));","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":4545451,"edited_by":4545451,"edited_at":"2024-07-03T20:47:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2024-07-03T20:47:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-07-03T19:30:17.000Z","updated_at":"2026-03-18T07:01:29.000Z","published_at":"2024-07-03T20:26:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Koch snowflake is an iteratively generated (fractal) shape built out of successively smaller equilateral triangles by following these steps: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDraw an equilateral triangle. (n = 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide the line segment into three segments of equal length.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDraw an equilateral triangle that has the middle segment from step 2 as its base and points outward.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eremove the line segment that is the base of the triangle from step 3. (n = 1) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat steps 2 - 4. (n = 2,3,...) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the limit of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \\\\rightarrow \\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e this shape has an infinite perimeter and a finite area. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026lt; \\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, this perimeter is calculable. Calculate both of these values for any input value of n and any starting triangle edge length, s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[A1,P1] = KochSnowflake(n,s)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"256\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"256\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"n = 0,1,2,3 of Koch Snowflake\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59856,"title":"Calculate the Area of the Ring","description":"\r\nYou have Ring which consist of inner and outer Circles with Radius r and R which are not given but you'll be given Hprizontal distance d which is Tangent to inner circle .\r\nCalculate the Area of the Ring","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 312.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 156.017px; transform-origin: 406.5px 156.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 231.033px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 115.517px; text-align: left; transform-origin: 383.5px 115.517px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"225\" height=\"225\" style=\"vertical-align: baseline;width: 225px;height: 225px\" 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2m1dDUbb4W355h/fCBVUbbXW8+pyjrqasJOQ4vWRD400u03rVsdThD/b3t7G3Clz7bLDZTu0rS8H/ok7K1u8RBB4H/ik9FDpxPV/Xx8fkxIj2wxu0yR3d/hifcSkxMjt727vA3wCZNf2HHUyoZTy/2JSYvrMmDNDGn638weHHm1rPn34U5b+aClYzFa2mkY9R8CaIdna1s8ppZJ3Ltw5pGBLAV0v7yoMX9O7X9IGprFz0U5VdrjsIq30/1HLbN51GcYaqpS6fsxvx5i+OF8d3h7elBeUM/uy2dba36+10TyglLqJpjnn1xiUoPg+cG3WvKzK10a+Fjy2P6wrV9cJIQUT/zLRUEHVE2flWO3eX+s3mGJFcvfk4XdsvMNsap3u/M35zJ442yrLKytSlroGZ3F1hNDQX5pyYVTLqPRrF15rNsXVNrMnz1Z7P967QwVUL5yR4xpR25Zwurb0qPF/GN/kDHhg3QFeH/W6VXa4LFtZahARA4aab5SlBlUUVax9Y/wb9v4VDbJJ3VVGPzJaqoDqAVxdm/fVyoTSJx/JGJthd5nSpVbiwp29y/fyxiVv2IHSwEYVVBcB+9zW1EQ5rC09wQ7Yy2ZPmm3v+7RpfcztLmpHxwkdlfTLX1OLKLM2JhylgmrQiF+MaFI9650LdzJn0hzbqrQ+UUE1Bsh3W1MTp0JberodsJfOuWyOvffjvW7rCSmjfzVaqoDqDcyo6XtqbEJhiJ8mX5BsdZncdFrB/Sv38/Y1byul1EJt66k4WbUiNDyV2tYz7KC9ZM6UOXb20my39YSM9he3J2Nshi198jfUsDWsqQm7oJg+7D+GmU1lrudI1hHeuvwtSym1Vtv6BpzFyREaj0pt6yuVpZa8dflb9q7Fu9zWEzJG/WqUcXw96fiaHF9TE/4oqmWU6jOrT92VhRGlh0qZPWm2FSwL7tGWvoLmufg6HHCMaKsP502fp/avbBqDNR3HdyS5Z7IlDHFfTY6viQlThCHuGfLAENOMqVHGvbCmsriSN8a9YZXklhxWQTUWKHBbUzOnUtt6hlb6s7emvmUVbi90W09IGPrjoaZWejrQ+XzH1sSEd0lDmgPvHVh/ZS5jB2zmzZhnF24rLFeWmgTkuK0pAgBBbetrguXB/XOmzrEqi7zfM+gzqw/+Fn4b+N75jj2fCU3plz/qfXNvoylsTVl2/zK979N9QtnqJmCT23oinEKBCqqrincVB9+d9a6tVa1WfoUdvlgffW/ta0qfvAsnL+xZOZ8JJ6mAajP4h4NDp84lvnn+G77++9cCzQ+AhW7riXBG1mulb961aJdc+/u1bmupN4O+PwhlqWRg5rmOO7cJJTcmdU+y0gZ5u5pS8e5ilt2/zEbyMvB3t/VEOCdvo3n6s0c+U/mZ3p6yTemVQodLOtiGzzjnAM25TBgjhby6z819PD0ao5VmwS0LLLvSPojifrf1RKgRD2mldy+8ZWFQWTVeghmWDLh7gGEH7WFAp7Mdcy4TzlBKxXp9WmLNE2vIXZUrj9cQCHkxjwgNQrm29c2H1h8yVj++2m0t9aLb9G6Y0aYCzlrD4qwmFIa4OW1gmtWya8uG0NYoHPzyICt+tUJprf8ArHRbT4RasRbNkysfW6kPfnnQbS11xhfro+u0rlL65I1nO+ZsJkxGM7nPLO+GolaFxYKbF1hIsoD/cltPhDrxiJBi23u3vWfZAdttLXWm58yeQgVVf6DrmV4/mwmnozEuuPaChlPWwKz53RoKtxUKFVS3EVmS5lUqVVDdkZ+Zb6z7wzq3tdSZLlO6YPgNBVx1ptfPaEJhiJvbjmqrEjK8WXPg6N6jrHlijdJa/w/wudt6ItSLlV4fLfW38NN5SmfOFpKeyYStUYzrc1Mfz25Z+uxXn2mtdDHwO7e1RAgJDwF7lty3xLMxaa+ZvaQKqoGcYZT0TCa8VkghvBqK5mfmk/lqJspSjwJNL6FJ86RcBdWDez/ea3h1R37XK7pi+A0NXHv6a982oWBimxFtlFeXqS1/cLkSUuTgFGWJ0HSYK30y67NffebJ1jAqIYpOl3XCMI1vTVWcbkIhDTmu4/iOnhwVzVmVw84FO6Wy1H8SGYxpaigVVP/l5daw+xXdpW3bg3CqW53gdBP2VZZKzBiT0XjKQsiKR1fY0ie34NQFjND0mCd9csuKR1d4chlNxpgM0EhgZPXnTzfhOOmTqv2o9o2nLEQc3nSY7CXZxvH6gJ78I0U4L0oF1YN7lu2R+z7xXpKo5AuSiU2NDQJjqz9/qgkFY9IGpSkvbt7d8MIGpCmLgDrVA4jgGd6Vfrll1W9XebJvmDEmwzRM46wm9Gx/MFgaZMPzGyxlqX8QSVXR1NEqoJ7as2SP9GI274wxGUIpNRiIqXquugl7K0sldxzXsfGV1ZNNr2wiWBoUwN/c1hKhUZiLJJD5WqbbOmpNxtgMtNI+YETVc9VNOFYaUrUb6bGS1xrW/WmdhWQhkaS9zYVjWut3N726yXPFWVP7pRKVEGUBY6qeO2lCyZjWA1srrxV52b9yP4VZhaa29TNua4nQiCjeLNhcYOZv9tZSNiEF7Ua1M4Qpvm1CKeW4juO81x/c8uYWpClzgSVua4nQqLwnTVmy+fXNbuuoNRljMgSaizhemrDKhMnKUq1bD2ztnrI6sm3+tqCy1HxqWRMuguepVJZ6c9Orm4Je+8unDUxD2zoG6AgnTXgBQMoFKW7pqhN53+RRklPiA951W0sEV3j12L5jvn2feWsoIKXnCZ/1hJMm7IGApB5JroiqKzsX7kQasgxY7raWCK7wmTTl/s3/8lZI2iKjBUaUYXO88asyYbeY5JigP/6c6RHDjh2Ldtga/TGRdaLNFa0s9ebWuVstL4WkQgpadmmpgO5QLRxt1adVXUpnu0ZZXhkHVh+Q2tbz3dYSwVUWVRypMA9nHnZbR61I7ZvqM0yjDxw3ofTLXsk9kj21iTd7WTZaa4DFbmuJ4CqfCyHsnFXeqmiQ1D0JLfSJcFRoW3dLviDZZVm14+C6g0i/3Ad4c19LhFBRKk253mtVf1N6pqCCKg1IkEA7bevo5B7eMmHehjylguprt3VEcB87aC/f+/HeoNs6akO1Rq+7BLqB0zx6ibxv8mw0G93WESEsWF2SW+Lz0oLuan7rLoEeQgrdsktL9xTVkvL8csrzy33QrE04A1gGFAHlOFWmHgK8mZekfnwBkLc+z20dNSY6KZropOggcIEEusa3i7eMKO+MyxzeeGIkrLma8HFgPhAA7gNuAj7ASXL8CeDNXJV1Z78QwirO9laVgxYdWgC0NYHUuNZxLsupHXkb8hCGqNS23ua2Fhe4DPhPnERW91R7/m3gPWAp8BRwd+NLcw1b+mRu0e6iDm4LqQ3RLaMlxwdmkmNSvbWV/vDGwwhDZAGe3F1dT/4DKMEJPU/nI5wlfLcBrRpRk+soW+0o3u2tljC6ZbSBIFEaPqN1TEqMcFtQbTi0/pClAuort3W4gAlcjBNyFpzlmLcAHzCqsUSFA9rWuwp3FHpqhNSf4McwjSQppGgVnRTttp5aUbyrGGCn2zpcIAWIBrLPcUzVa97L1lU/9hTvKfZUY+Jv4UcIkSCVUkkxKTHnf0cYESwLCpyQLEKEKnYFjgbMyiLvLCOOSohCC50ota0TPNUSalABJXGG5ZsbBTiJrDqd45iq15rbSqI9AMV7vNMv9Lfwo20dJ7XSfi+lOLQqLLTWAihzW4sLWMBnOHkrz7b581ogCKxoLFFhwiFw5pC9QlRCFFrpeAloL20DscpP5PbxzqcdWv4AxOPMFZ7OOGA68BJnH7hpqgQBvFTj3p/gRyttmgi0VtozHdpg2YkBsObYEoIzKf9bnLnCzsAbOP3j0Tjzhl8CP3VNnXtY4DETtnD270qBiLSE3uMh4EqcKYs/Aa8BE4H/xglVj7qmzD08Z8KohCgAnJZQe8eFkZbwBO/gzBc+BRQCv6B51+DwnAkNv7NU1AS0Vt4xYbWWsLmbECAduAPnBhwI3MzxAYpmiOdMGCgNAM6mXk+Fo9VawuYcjp7OPTjp8zYBU13W4hYWgLa8czMHS517WXotHJXGiVQ43plXaXi2A4NwFm8vxOkneiuVev1JBIhKjHJbR405aUKPhaOxrU9sl/NepuKG5RhwI87i7btw5gk7uainsUmDU+6PsCdYGkQIYXsuHI1LO7HtKs1NHWHMKziLt5OBdTSf8DQNTrk/wp5ASQAhRYUUQgTtgHd2BEUnRSNNqYFUt7WEMV/T/MLTVPBeS4ikXApDFJTleWigUUB0UrRFpCU8H80tPE3zxfpsLy3BDJYGEVKUSmxyS/NK3dZTK2LTYyHSJ6wp1cPTL2i64WnrmNQY74R0OCbUWpdI27IPlB4q9c7kChCfHm8QaQlrQ1V4uoSmG562jkuP81QW+WBpEKFFiQTySnJLPPUN0qp3K2n4jUFu6/AYTTo8FabonNA+wTuxKI4JlVLHJHCo7JCH+oRAm6FtsAN2B5wQK0LteAVnsXdVeHq5u3JCg0AMSO3nrbG64r3Flrb1IQkcqiisMLXtnXmKNsPaAAhgqMtSvMpXnAxPF+D98LSTslRC2iBv9VAKthQIYKsEDmmlRXmBd1aBJXVLwh/vt4iYsD6cKTzt7KagejAAnAq4XqH0UCnBkqABZEkgD8BTI6QC0ganCSHEELelNAGqh6fr8GZ42j8qMcpq0b6F2zpqTOG2wqp/bpPAboDC7YVnfUM40nZYW0OYYoTbOpoIXwGDcSb3PReeCiEGpg1O89TIaEFWAQg0sF0CB6Qpj+Zn5rutq1akD02vKi3Vxm0tTYSjwA04OzK+h3fCU0MY4pJ2I9p5yoSF2wqRPnkQKJMAGr3h8IbD3hmZAdoOa1v1z2Fu6miCPAuMxDvh6WhlqcRu07u5raNW5G/O19rWmXC8Uq+29Ma8DXmeyl6c0DGhavnaRW5raYJ4KTydGp0UbbUZ4q2AqGBrgaVtvRVO1qzfVLSzyOelhdwAPa7qYUq/vNltHU2U08PTlTRMePpLQFd7FAGfH7/2eZF+eU33K7ubwvBMrjLsgE1xdrEJnGpCZSlxZNsR95TVgR7X9EAFVHugv9tamjBV4WkSDRue3gxcAfwIqMTJIjfzPO/prgKqa7dp3gpFi3YVoW0tgCyoZkIArw3OdLq0E754nw1c47aWJk5jhKcf4qxrfQWYDOQD3z/Pe6ZJn1SdJnUKsZSG5UjWicbuFBMekT5Z4DUTGlEG3ad3N6Rf1ih0iVAvGis8BSgFNgNdznWQMMX0Dpd0wB/vbyAZDcORrCMIQ5RzvFTBiWFdrfTG/E35nhohBeh+ZXdUQHUHeritpZnQGKOnAuiA0xqejTQUo7td0c1TUxMAR7YdQRhiN04fuJoJbb1m36f7LC+lugDoOrUrvlifDdzptpZmRNXa0+rhaX2bozic9P4ZOLlUOwEvnOP4O6QpRe+betfzso3P3uV7gyqgVlf9f/VvkSXlBeW+vA15LsiqO744HwO/P9AQhvgBxzNuRWgUQj25n42znnUv8BPgYeCZsxxrSFPe12dWH8NrZf2Ks4sp2lnkwylnAJxqwlVCiso9y/Y0vrJ6MuSBIQhENHC721oamHCsYReq8HQaThXiG4FMnKTGZyv5fbmyVPqAewbU8VLusWfZnqrlah9VPVfdhBUIVu5euttTu+wBWrRrwQUzLxDSlP8BGG7rCRF/xZlHuhL4BmfY/h43BZ2DUISna3Fa0zeBSTgGfPpMBwpD/KD1wNZWm6HemqAHyF6araUpN1CtatYpnVpt64/2f7Jfq6DnfMiQ+4cIZan2ON+oTYX2wKPA/UBXYJ6ras5NKMPTXOBJ4Cag32mv9UAxYeD3BnpqFz0AGrKXZFsqqD6s/vTpI0sfBsuCRu6a3EZUFhrajmhLu1HtbMNnPOi2lhASB9wKLMcZzt7nqpqaEarw9E84hW4erf6kMMQfWnRoofrdfro3w5+8DXmUF5T7cOZET3C6Cb+SpjyWvSy70YSFkuE/HW7YQXs4MNxtLSHiCLDBbRF1oCo8XUbdw9OjOKOkV3F80y4wTtt62tjfjjWrKhp5ieyl2QgpKjmtivLpJrS1rZdnL8321iLS43S7ohsJHRMsYYiH3dYSIg67LaAeHAWu5/zh6RM484JnmhP8Hc49uh7AMI3/btW3ldXrhl4NobfB2fPRHoVkDVBR/flvTXRqrT/MXZMrK49WNpq4UCEMwcQ/TzS1racBU9zWEwH4dnha1z77NbZlj5z4l4mmkN5ZrF2FXWmzZ9kerS39/umvnWm1wcfa1iJnZU4jSAs93aZ3I2NMhpJ++TSRyk3hQvXw9F1qH56a0i+f6DC+g+pwSYeG0NfgHFh3ALvSNqg2NVHFmUy4WZoyZ+ucrQ2vrIGY8OcJUlu6O04YFCE8qB6e3kPtRk9vV0HVbdz/jPPcErUqdn+4G2nKozhfSKdwpl9KK0u9tGX2FruqfprXaN2/Nf3v7C+kKR8nkps03Kgenn7N+XfAxEmffLz3Db11+uD0BhfXUGS+lhlUlpoPfGu85WzfLC9b5ZbMmpfVoMIakov/+2LMaDMO+K3bWurID4GebotoIL7ECU8/AOZy7vD0YSBlzONjvNcRPE7u2lyKdxf7gNfO9PrZTLhdmGLthhc3eHKUFCA2NZaxT4w1gbtx9qdFCC9qEp5eLIT4+ehHR8vEzt5dFpz5WibSlHmcoT8IZzch2tLP7ftkn1G0s6ihtDU4g34wiK6Xd9XSlP8iUkAmXDk9PL32+PMp0pRzMy7J0CN+6d3MlnalTeYrmZay1EucIRSFc5gQmCOkKN/06qYGEddYTH1xqoxKjGohDPG821oinJXq4ekc4E/CEP/0xflSpr06zfDilEQVuxbvovJopQm8frZjzmXCEm3r+Zte3hT02h7D6sSmxjLxryfmDr/jtp4IZ6V6ePp9bevpox8dbbZo552s2mdi8xubtfTJLM6x8ul8Q74vF2cX+/av3B9aZY1Mrxt60fvm3lpI8SxNZ0lbU+VjaciAP97PikdXkPWWdwcHK49Wsn3+dq2C6qVzHXc+Ey6Vpjy06WVvh6QAU56bIloPbG1IUy7ESZ0QIfxIkT75QYuOLfx3br6TzpM6M/+6+Sy9fyleS8cJkPlqJiqgAP51ruPOZ0JbWer5zNcz7UBJIGTi3MCMMbl+8fVGfLv4ltInlwIt3dYU4RRihSmWRCVEZdy47EazRUYLZsyZwWV/v4z1f1/Pa6Neo3h3sdsaa4yyFGueWGMJId7CyRZwVmqyAuFlq9yS2/69LTTqXCSmVQwzF800jSijizDEHCLL2sIFKYR4RRrywpnvzzQTO52cjhhw9wBmrZpFxZEKXhz4omfC023/3sax/cdMpdST5zu2JibcbpjGum+e/8Z78cAZaNW7FZe/dLmhlZ4IPO62nggAPKTR10x+drJxpt3y6YPTue3r2zwVnn7+x89twzTW4FRDPic12pSllT5ydO/RGzpN7ERCh4R6C3SbVr1bYUab7Fm6ZxTOZ/Cx25rqSCuclTUvAd5LDuTwPeCpkQ+PFEN/fPaar2aUSc+ZPYlvE8+qx1ax872ddJrQieik8Eu7k7Mqh1W/WSW10j/ieKr7c1HTnZFZwhQ3HNt/LKnPrD6eXURbnfaj22NGmexZtmcsTgKlZW5rqgNeN+EDwF/63d5PTHh6grOr8DykD06ny9QuZL6SyRdPf0FStyRa9T5bPih3WHr/UlW0s2iPVvr7cP4JvpqaUKMoKNpRNLPr5V3x+txNFe0vbk98m3h2vbdrFNAWWEQNPrQwwssmfAJ4bPjPhouJf5lYIwNWEd82nn6396Mgs4AVv15BxZEKOl7aEWm43z4UbClg6Y+WCm3rX1CDUBRql5lsi/TJWaWHShN73dDLu0sYTiN9SDrxbePFzoU7ByFpj2Yh3jGiF00ocDLJ/XjsE2MZ/evRtTJgFWaUSc9rexKdFM2a360Jm/D0s//6jLz1efla6e9wlmVqp1Obrw5bBdWTO97ZIaoVtGgS9L+rPxP/OlGguQMn4Wy41uLzOgL4A/CDsb8by4hf1HNNqIAh9w9h1kpn9PSlQS+5OnpaXlDOppc32cpSf8dJUVkjapstZ5M05d2VxZVxPa5sWqUf2gxtQ2LHRHYu2jlIGnKSVnoRUOK2rvPgpZYwSRhitkDcOulvk845CFNbwiU8/fQ/PyVndU4AzU04RW1qRG1NaGmlg4c3Hr6s2/RuIr5NfC3fHt6kDUijy+QuYseCHelWuXWbVno155lodRmvmHCY9MtPohOjB1z9ztVGr+tDn6jJ7fD0SNYRFt22SGmlHwfeq8176/JV8VdhiC0f3POB7ZmeUy1oM7QNd2650+x6eddkIcQnOHkv3e/xexMJPCqkWN1xXMf0u7beZXaa0KnhruZieLrkR0tsBLnA72v73rokb9Ra6S0lOSW3t+zcktYDWtfhFOGNGWXS6/pe0ogxxN5le8cKUwxFsYjTUtWFAeHcEqYJUywQQtw6/n/Hy4l/mSh9cY3T1W7s8HTX+7uq5gXvwilZUCvqmkE1WxhiUM7qnK4D7x0oz5uI9VwtZriOswpnLjH1wlSx490dXYBrtdIbCK+bPVxNOET65UdRLaJ6X/321Uafm/s0+t+5scJTbWv+ffW/rUBh4Eut9I/rco46fzVoWz9QllemVv9u9TkOch76tP++dUwY0+OqHtz25W1G2sC0rgiWS0O+RmSX/tnwAw8KQ6xuO6xt2zs23mF2ntRQxXxrQCOEp9+88A0FmQWGbdk/oo53c31yiReh8R1Ye+Di3jf1FtHJZ/6G0Y4LT0VU/RDfei4ciWkVw4V3XChatGvB3uV7e2tL36u1rkpf5+bXSDi1hJOlTy5CcM2IX44wLn/pchGVGOWyJIf4tvH0u60f+Zn5rPzNypCFp5VHK5l3xTzLqrRmo/lzXc9T34T+nwshbi/aVRTf+8bep9hI6zOYrzqnGzGMTQgghCB9cDr97+ovyw6XRR1af2iq9Msrta2/AtzKlBwOJuxk+I1Xta1/0350+8RrFlwje9/Qm3BLSWFGO2tPQxmernxkJXs+2hNAMR0nM0CdqG9PtUxZ6oEd7+6Quz/cffJZDShOhKOnPKofAyfD0zAPS6uIaRXDlBemMGvFLJJ7JPdGsAZ4DujutrZGpjuSF4QU26OToidPf2M6N31yk0ztm+q2rrNzhvB069y6Jbku2lXE5//7udJK/x6nYladCUVpm82GaYzLWZPTfuA9A6UwBFrrM7aEQpyh1RPeaQ2rk5CRwIC7B8iYpBhxcN3BflaFdb8QYhBObb3GapXcaAn7S0P+GXgmJiWm/6hfjTKnvTJNeikxb73DUw3vznpXFe8sztNKXw/UK0t2SOpLaaXXVR6pvDeqZZRsd1E7tKXR6mQLJxynAWcwovBO3/B0hBS0HdGWIQ8MMRI7J4oj2450Lc8vv0P65JVa6aM421gasuJqY5rwIiPKeF4r/VR82/ieY347xpj2yjTZ4ZIOGFHeK1NWn/D0q799xZd//hKt9I3A5vpqCeUt/0cz2nzgtq9vI7FTotMKiuOmq/YTzmNED5nwW2in5sDaJ9daez7aY0pD5ipL/RF4AafgZajpCWwBxgKfNsD5k4GZht/4rh2whyV1T7JHPjTS6H1Tb6Sv6axfOPjFQd65/h3K88uZ/Pxkes48e+Lz/Mx8Xhr0km0H7P8D7gvF9UN5y8dKnyxN6ZXCzZ/ejDAEQh5/nGbEJmvCahzeeJh1/7tOZb6eiba1RvCRtvVcYD6hqzvYECaMBqYJQ9yKZoqQQna9vCv9bu8nu13RLewGXEJFZXEl79/5Plnzshh832DGPTmO0+e/rQqLl4e8bB3ZdmSHCqpBQHkorh3qT1QLKRj+i+GM+MUIpCEdMwoB8gytYRM2YRUlB0rIeiuLrXO32jkrc6TWWgtDrNCWnoNTxbY+a1NDZcJuwAQhxARhiMnKUnFpg9Lsfrf1M3rf2JuYVjH1OLWH0PDFn79g+c+Xk3phKjNmz6Bll5YnXl72wDK+/MuXAa30EGBjqC7bELe8RsCdmXfSon2LM7aI0HxMWJ2yvDK2zd/G1rlb2ffxPpStkIY8omy1BqeAZtUjr4anrIsJ/UAfoB8wRvrlZBVQ7aQpVZvhbVSXy7qYPa7uQas+4bVbvTE5+MVB5l83n4qCihPh6a7Fu5g7dS5oHsApYBMyGsSEwhC0vrA1N318E8J3BhNWma45mPB437j6/2utqSyuJHtpNgfXHSRndQ4HvzqIVWYBIE2Zqyz1NbAbZ8Al+/jPguNnqQTKcKZF1nLShAJIPf5oDaSf+Lekh+EzBqqA6qy1NoQhdErPFKvzZZ19nSZ0ImNMBo21ttMLVA9P+9/Zn21vb7Mqiio+0paeTIgn1BrqltfSlHSZ2oUZb844acDjffl6tYKn39RhjgqqU2ZjhRSgnDWHJQdL2Pb2NnYt2kVJTglH9x1F2QplKbTSaLvaKHM9OPElaIgTXQRpSE99jm5hVVhY5RbCECXa1t2AQ6G+RkP+GTQCRj0yiosevOikEatftS4toMdMeEaqLVywgzb5W/MJFAU4uv8odtCmZH8JWusTAwPBkiAVhRVYlU5LqYMa23IyJ9gBG22fNKov1oc/zo8ZbxIVH4UR473pg3Aid3Uu29/ZroGZwLyGuEZD387aiDa4ZeUttOrX6uRkaF3Dz6p7zesmBKeFE46JAkcD+Fv4kT6JkILKY5X4o/1If9OZBvAihzcd5uXBL4d0OuJMNPRfOQoLZk+cTUlOyQkTCQRa6JNmqmnEdbw/6XU02okKNJQdKsMf58fwG87nYmsMw0CYTeAX9TClh0qZO2WupbXeBvy8Ia/V0CYM2JbdqvJYJf8a+y/KC8pPzDMJ7c1VMqGgalBKSEFShySiY6MxpYk0JNKU+GJ8TXY+zgtUFlfyxrg3rNKDpYdVUE3g1PnAX3LqauggzgDaX3FWMNWaxoh3ClRQdS3JLWHelfOwKqwm06KFAoXCwsLGPrmYPRKFuoayFPOvn68KtxdWKktNwlkLfCZuBq4ArgNeAe4A5tblmo3Vay/USr9fcqDk1oItBeYF115wcpAmwgk0GoFA2c7o6Plaw3nT57HgpgXEtY7jTDUcwpVn2j9DWV4ZDZpvpo4svnux3vbWNq2VvhJYdYZDRgMTcIqZrsdZH7wciAdm4aTMLKvNNRvzO/dzbetbsuZl6U8faohljt6narCqKiw9F+X55exavAszxsTrJc3Dhc+f+pwNL2wQWut7gMW1fHtVMt5aT7Y2duAzF82Da55Yw9fPfN3Il25abHlzC9rWXPybi8ldk0vhjoZYH9582PzGZj7++ccATwLP1+AtcTitXxIwDmf09BPOHr6eFTd6H78Hnlly3xK9Y8EOFy7fNNj06iYyxmTQ/+7+GFEGma9mui3pjGx6ZRPPdn+Wp6Kf4pVhr5Cz2q0kBGcnZ1UOi25bpKSUbwK/qOHbsoFjOC3gR8ABnP5hrXFrCODHSD5996Z37f0r67UpuVlyZNsRDnx+gJ7X9SQqIYrOl3Um87XwM+Gu93fx3nfeI31wOle/fTV9bunDO9e9Q+XRGmeIb3AKtxfy76v+bWmlNyhb3UnNJ8ymARcDlwDfxan8vBiIra0Gt0wY0Ja+wqqwVs2eMNve85HbOYq8RearmQhD0ONqpxRBr+t7UbSriHD7Qlvx6AraDGvD9Den02VKFwbfN5gxj48hcCw8Sq8XbC3g1ZGvBsuPlO9WlppKLVLX46zZXYETgr4IXA8MxBklrRVuDoYf05aeYAftBXMum6OaQjnuRkFD5muZZIzJIC4tDoBu07thRpthFZKqoOLglwfpdcOpKe97Xd8rLKanDqw7wCvDXrEqiio2aksPxwkn60PVDvsLa/tGt2ekAtrW16J5Y/7M+XrTK5FRvvOxf8V+irOL6TKlC5VFlVQWVaItTcfxHdk6Z2vYlJEuzStF25r4tqfWKzGiDGJS3N2fmLs2lzcvfdO2y+312tKXEpqsB4OO/6z1hm0zBBevL7ay1XeQBBfdvug7ylLiwu/W+suk2VA1HbH858tZ/vPl33p958KdJ8JUN4lrHYeQgoojp1YO0EpTWeRenzBndQ6zJ822VYX60rbsSUBxHU81CSfNoQF0Bn6CE86+VNsThYMJAWwUd2o0i+9a/B0gYsQzYFfabJ27lY7jOzLyv0ae+qKGf1/9bza9uiksTCh9kvTB6WQvyWbgvQNPPL93+V6U1ZC5r85O7tpc5kyaY6kKtd627MuouwEBXj/+U+NMS6zBKR5U635VuJgQnKqmd2ily9+/8/17rXKLQT8YdN43NSd2LNhBZVElg344iA6XdPjW671v7M2GFzZQcaSCs2VEb0xGPTKKedPn8eVfvqTfbf0o2lnE0h8tdSU7W9a8LBbcvMBGUdUC1jVZ7xPHHyEj3DabaZy68S12Ldo1wvAZIuPijLDoyIcDnzz4CeUF5Uz+x2SE8e0PJbZ1LOv/vp7ETolhsYwtuUcyCR0TWPs/a/ns4c/Y9+k+xjw+hn3L99H6wtaNs2xNw+rfruaDez9AK/2WtvVV1G4UtMEJ59v7MeDhntf3VFP/OVX6YiOpFyLUDqvC4v073teb/7UZ4NfAbwjDXO/hbEKA6cIQ/0rslBh17cJrzZSeKW7rieARju49ytzL51pHthypVLaaCbzvtqazEe4mBOgpfXKBL8bXacbcGe6W2orgCQ6sO8Bbl79lVRRWHDo+Cb/BbU3nItz6hGciXyv9prLURZtf35wR2ypWhEN/J0J4smPBDt66/C0rcCyQqW09Htjutqbz4QUTApSheQ1N0s5FO4eX5JToTpM6ifNt94nQfLArbT7+6ccs+/EytNILtNKXczJFZFjjhXD0dG4VhniuZZeWctqr08y2w9u6rSeCyxRuL2T+zPnW4Y2H0Ur/HHiaMByAORteaQmr8w2aOcGjwYu+ef6bNnbQFu1Ht6931dUI3mTz65uZO3WuVXKgZJ9WejLwb7c11RYvtoRVGMDPhBS/SemTIqe/Nt1IvTCMC1RGCCmlB0tZct8SO+utLAPJmyi+Rz2q5bqJl01YRT/pk/9C03v0r0fL4T8fft7UEBE8jIYNL25g2f3LgsHyYKG29b14sPWrTlMwITit4k+FFI8l90qWV7x6hZE2MM1tTRFCTH5mPou+u8g6sO6ARPMkzuR7rZIqhSNe7BOeCQ2sRLO4sqhy/IYXNrQUhpBthrRpUsUsmysqqFj75FrevfFd+1jOsRwUM4HnqGeZ6nChqbSE1YlB8juhxX1xbeL0uCfHGb1v7N00f9NmwL5P9/HhDz60CjILpNb6T8DDNIHWrzpN+da8UJjiaW3pcelD0u0Jf5pgtBvZzm1NEWrIoa8OsfzB5Sr7w2wpfXKzCqrv4qSUaHI0ZRNWMV6a8mllqX4dL+2oLn36UpnaNzKKGq7krc/jo59+pPYs2yOlX2aqgHoAWOq2roakOZgQnISs9wgpfi0MkTDsJ8OMoT8ZSmzrWifGitBAHMs5xspfr9QbXtighRCHlK0ewdml3iT6feeiuZiwiiTgYWGI70spfX2/01cO/clQkdIrsjvDLcoLyln7+7V88acvbK30UWWpx4D/AyrO996mQnMzYRXJwL3SkA8opVp1mdJFDfuPYbLj+I5u62o2lB4s5eu/f83nT31u2ZV2pbLUEzjLzUpcltboNFcTVhEF3Cqk+KlWukerfq2CF/3iIl/P63pGpjYaiJxVOXz5py+trH9nSa10uVb6GZx0EUfO996mSnM3YXVGC0M8qG09JTop2h5w9wBz8P2DiW8Tf/53RjgnFYUVrH92Pev/vj5QnF3sF6bYqC39FDAbCJ903C4RMeG3GY7gZ8DVvhif6jOrj9Hrxl5kjMmIFO6sJblrc8mam8X6Z9cHAyUBQyAWaq3/ijPa6ZldDg1N5K46O12B70lTzlKWahOXFmf1vqm32euGXrQZFtlUfDbyM/PZ/MZmMl/LtI7uOWpKUx5RlnoOZ7AlUu/gDERMeH4kMAq4QRjiBm3r5ISOCYG+t/T197qxF61616lCcpOicEchWXOz2PjKxsCRrUf8QooSrfQ84E2cVs9yWWJYEzFh7TBxqrTeKA15jbJVXFL3JKvThE5m50md6TC+A1EJUW5rbHDKC8rZ89Ee9izdw67Fu4JH9x71CSkCWuuFaF7HSVvZbKYY6kvEhHUnGrgcmCENOUnZKk0YQrcZ1sbuOqWr2WliJ9oMbXPG/KBew6qwyFmZQ/bSbHYt3hU8/M1hU2sthCF2alu/D3wIfEwznF4IBd6/Q8KHXsAEYYiJQojxylJxRpRhp/RKUemD0n2t+rYitV8qqX1TiUuPc1vrWbEqLPI35XNo/SHy1udx6KtD6uBXB7ErbSlNWaJtvURr/QHwAU6hzAj1JGLChsEABh9/9BemGIimr7Z1LEBUYlSwdf/WtB7Q2pfaN5XUfqm06tMKfwt/owksLyin5EAJx/YfI39TPnnr83TuutxA0c4iv7a1AJCG3KNs9SWwHlgGfE6kfxdyIiZsPARO9Z7+QD8hRH/pl0PsgJ2BRiAgumW0FdMqhpiUGBmbGitjUmKITo4mJiXGeTiv1cisFYUVlB4o5VjuMUpySyjJKdHH9h0LHs05SvnhctMO2CdWIwghghhs0ZauMtw3x3/Wp2BKhBoSMaH7xAF9gX5AG5wldSnCFK0Nw0jVQrfStk5SQdWiLicXUpQJQ+RqS+dorfcBB4Gcaj8P4EwdNPmF0uHK/wPZNSYTJpfCYAAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.067px 7.81667px; transform-origin: 192.067px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have Ring which consist of inner and outer Circles with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.742px 7.81667px; transform-origin: 126.742px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRadius r and R which are not given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.1833px 7.81667px; transform-origin: 59.1833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.81667px; transform-origin: 96.5917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the Area of the Ring\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(d)\r\n  area = d;\r\nend","test_suite":"%%\r\nd = 3;\r\narea_correct = 28.2743;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 5;\r\narea_correct = 78.5398;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 8;\r\narea_correct = 201.0619;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 15;\r\narea_correct = 706.8583;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 17;\r\narea_correct = 907.9203;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4033021,"edited_by":223089,"edited_at":"2024-06-12T15:22:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2024-06-12T15:22:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-07T14:03:59.000Z","updated_at":"2026-04-18T06:50:15.000Z","published_at":"2024-04-07T14:20:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have Ring which consist of inner and outer Circles with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRadius r and R which are not given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the Area of the 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the shortest distance between a point and a straight line.","description":"Given the Cartesian coordinates of three points A, B and C (in a flat Euclidean space),\r\nfind the shortest distance between the straight line through A and B, and the point C.\r\n\r\nAssumption:\r\n\r\nA and B do not coincide.","description_html":"\u003cp\u003eGiven the Cartesian coordinates of three points A, B and C (in a flat Euclidean space),\r\nfind the shortest distance between the straight line through A and B, and the point C.\u003c/p\u003e\u003cp\u003eAssumption:\u003c/p\u003e\u003cp\u003eA and B do not coincide.\u003c/p\u003e","function_template":"function y = shortest_distance(x1,x2,x3)\r\n  y = 0;\r\nend","test_suite":"%%\r\nx1 = [0 0 0];\r\nx2 = [1 1 1];\r\nx3 = [2 2 2];\r\n\r\ny_correct = 0; \r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\nx1 = [0 0 0];\r\nx2 = [0 0 1];\r\nx3 = [1 0 0];\r\n\r\ny_correct = 1;\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\nx1 = [1 0 0];\r\nx2 = [0 1 0];\r\nx3 = [0 0 0];\r\n\r\ny_correct = sqrt(1/2);\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\ntheta = 0.5;\r\npsi = -0.2;\r\nphi = 1.1;\r\nR3=[cos(psi) sin(psi) 0.0; -sin(psi) cos(psi) 0.0; 0.0 0.0 1.0];\r\nR2=[cos(theta) 0.0 -sin(theta); 0.0 1.0 0.0; sin(theta) 0.0 cos(theta)];\r\nR1=[1.0 0.0 0.0; 0.0 cos(phi) sin(phi); 0.0 -sin(phi) cos(phi)];\r\n\r\nR = R3*R2*R1;\r\nx1 = [1 0 0]*R;\r\nx2 = [0 1 0]*R;\r\nx3 = [0 0 0]*R;\r\n\r\ny_correct = sqrt(1/2);\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)\r\n\r\n%%\r\nx1 = [0 0 0];\r\nx2 = [0 0 1];\r\nx3 = x2;\r\n\r\ny_correct = 0;\r\neps = 4.999 * 10^(-7);\r\nassert(abs(shortest_distance(x1,x2,x3)-y_correct)\u003ceps)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":393995,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-04T14:23:13.000Z","updated_at":"2026-03-19T07:20:29.000Z","published_at":"2020-02-18T12:21:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1.5 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2.7273;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[7 3 11.3];\r\ny=ratio_polygon(s);\r\ny_correct=7.91;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[121 125 17.37];\r\ny=ratio_polygon(s);\r\ny_correct=8.5438;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[19 3 25];\r\ny=ratio_polygon(s);\r\ny_correct=21.5909;\r\nassert(abs(y-y_correct)\u003ceps)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-21T18:12:43.000Z","updated_at":"2026-03-24T12:20:14.000Z","published_at":"2021-01-21T18:12:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a square sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"282\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"287\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the 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many points lie within the rectangle and how many aren't?","description":"Suppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as *input-1, R* i.e *R=[Bottom-left corner co-ordinate; Top-Right corner coordinate]*. And you are told to count the points of the *input-2, P* (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. *Show them collectively within an output matrix, Y.*\r\n\r\nExample: *Inputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];*\r\n","description_html":"\u003cp\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as \u003cb\u003einput-1, R\u003c/b\u003e i.e \u003cb\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/b\u003e. And you are told to count the points of the \u003cb\u003einput-2, P\u003c/b\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not. \u003cb\u003eShow them collectively within an output matrix, Y.\u003c/b\u003e\u003c/p\u003e\u003cp\u003eExample: \u003cb\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5]\r\n         Output: Y=[1 1];\u003c/b\u003e\u003c/p\u003e","function_template":"function Y=PointsWithinRectangle(P,R)\r\nY=1;\r\nend","test_suite":"%%\r\nP =[1 0;1 5;5 5;-1 2;5 -4];\r\nR=[0 0;10 8];\r\nY_correct =[2 3];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 2;-1 4];\r\nR=[-1 2;3 8];\r\nY_correct =[0 2];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 4;2 -4;6,-6;4 5;1 2;8 9;1 1;0 0;-1 -2;4 5];\r\nR=[-1 4;2 8];\r\nY_correct =[15 0];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[1 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;2 0];\r\nR=[0 0;10 8];\r\nY_correct =[9 12];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))\r\n%%\r\nP =[11 0;-4 -5;46 2;8 9;2 3;-2 3;2 -4;6,-6;4 5;1 2;-1 2;1 1;0 0;-1 -2;4 5;1 1; 4 2;7 8;1 -1;0 1;22 0];\r\nR=[0 0;10 8];\r\nY_correct =[11 10];\r\nassert(isequal(PointsWithinRectangle(P,R),Y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":430818,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2020-05-31T08:14:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-30T08:08:12.000Z","updated_at":"2026-03-31T13:03:03.000Z","published_at":"2020-05-31T07:15:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose, you are given the coordinates of bottom-left and top-right corners of a rectangle as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput-1, R\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e i.e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR=[Bottom-left corner co-ordinate; Top-Right corner coordinate]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. And you are told to count the points of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput-2, P\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which represents multiple points a,b,c,d, etc within a matrix i.e P=[a;b;c;d]) lie within the rectangle, R and how many are not.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eShow them collectively within an output matrix, Y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs: R=[0 0;10 8], P=[1 5;-1 5] Output: Y=[1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54124,"title":"Area of a regular hexagon","description":"Given the length of a side of a regular hexagon, return its area rounded to two decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven the length of a side of a regular hexagon, return its area rounded to two decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hexagon_area(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2.6;\r\nassert(isequal(hexagon_area(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 64.95;\r\nassert(isequal(hexagon_area(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = 259.81;\r\nassert(isequal(hexagon_area(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":1985600,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T19:42:05.000Z","updated_at":"2026-03-23T10:21:34.000Z","published_at":"2022-03-04T19:42:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the length of a side of a regular hexagon, return its area rounded to two decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; 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sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n  T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n              3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n              1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-04-17T01:06:41.000Z","published_at":"2025-07-23T16:40:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh, that is to say give one triangulation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"335\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"447\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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the area of the shoemaker’s knife","description":"A shape resembling a shoemaker’s knife is constructed from a semicircle with diameter  with two semicircular “bites” of diameters  and . \r\nWrite a function to compute the area  of this shape as well as the area  of a circle with diameter , the length of the line tangent to the two smaller semicircles and touching the edge of the largest semicircle.\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 399.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 199.85px; transform-origin: 407px 199.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, 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italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.625px 8px; transform-origin: 97.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with two semicircular “bites” of diameters \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a-b\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.608px 8px; transform-origin: 114.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ak\" style=\"width: 17px; height: 20px;\" width=\"17\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.85px 8px; transform-origin: 103.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of this shape as well as the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Ac\" style=\"width: 16.5px; height: 20px;\" width=\"16.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a circle with diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the length of the line tangent to the two smaller semicircles and touching the edge of the largest semicircle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 266.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 133.35px; text-align: left; transform-origin: 384px 133.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 417px;height: 261px\" 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\" data-image-state=\"image-loaded\" width=\"417\" height=\"261\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Ak,Ac] = arbelos(a,b)\r\n  %  a = diameter of largest semicircle\r\n  %  b = diameter of medium semicircle\r\n  %  Ak = area of the shoemaker's knife\r\n  %  Ac = area of the circle with diameter c\r\n  Ak = polyarea(a+b);\r\n  Ac = pi*c^2/4\r\nend","test_suite":"%%\r\na = 1; \r\nb = 0.45;\r\nAk = arbelos(a,b);\r\nAk_correct = 0.194386045440868;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = 1; \r\nb = 0.37;\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 0.183076311887945;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%%\r\na = 2; \r\nb = 1.1;\r\nAk = arbelos(a,b);\r\nAk_correct = 0.777544181763474;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = 2;\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 1.128274457746991;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 0.45;\r\nAk = arbelos(a,b);\r\nAk_correct = 0.901244392498572;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = pi; \r\nb = pi/6;\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 1.076606829177077;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(17); \r\nb = sqrt(10);\r\nAk = arbelos(a,b);\r\nAk_correct = 2.386357557750292;\r\nassert(abs(Ak-Ak_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(31); \r\nb = sqrt(29);\r\n[~,Ac] = arbelos(a,b);\r\nAc_correct = 0.772304555883422;\r\nassert(abs(Ac-Ac_correct)\u003c1e-13)\r\n\r\n%% \r\nd = [3.5 8];\r\nfor k = 1:4\r\n    [Ak,Ac] = arbelos(d(k+1),d(k));\r\n    w = rand;\r\n    d(k+2) = w*Ak+(1-w)*Ac;\r\nend\r\nd6_correct = 2.568944500499240e+03;\r\nassert(abs(d(6)-d6_correct)/d6_correct \u003c 1e-13)\r\n\r\n%%\r\nfiletext = fileread('arbelos.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-16T01:00:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-16T00:57:58.000Z","updated_at":"2025-04-28T19:56:12.000Z","published_at":"2023-01-16T00:59:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA shape resembling a shoemaker’s knife is constructed from a semicircle with diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with two semicircular “bites” of diameters \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a-b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea-b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ak\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of this shape as well as the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Ac\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a circle with diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the length of the line tangent to the two smaller semicircles and touching the edge of the largest semicircle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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lines","description":"Check whether two given lines are orthogonal or not.\r\n\r\nTwo lines are orthogonal if they create a right angle at their intersections.\r\n\r\n* p=[x1 y1; x2 y2]   \r\n* q=[x3 y3; x4 y4]\r\n\r\nhere (x1,y1) and (x2,y2) form a line.","description_html":"\u003cp\u003eCheck whether two given lines are orthogonal or not.\u003c/p\u003e\u003cp\u003eTwo lines are orthogonal if they create a right angle at their intersections.\u003c/p\u003e\u003cul\u003e\u003cli\u003ep=[x1 y1; x2 y2]\u003c/li\u003e\u003cli\u003eq=[x3 y3; x4 y4]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003ehere (x1,y1) and (x2,y2) form a line.\u003c/p\u003e","function_template":"function tf = ortho_line(p,q)","test_suite":"%%\r\np=[7,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,3;0 13];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,3;-1,0];\r\ny_correct = 0;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[0,4;0 -9];\r\nq=[2,0;-1,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n%%\r\np=[2,2;5,5];\r\nq=[0,-2;-2,0];\r\ny_correct = 1;\r\nassert(isequal(ortho_line(p,q),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-26T06:07:02.000Z","updated_at":"2026-03-05T16:46:12.000Z","published_at":"2020-01-26T06:07:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck whether two given lines are orthogonal or not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo lines are orthogonal if they create a right angle at their intersections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=[x1 y1; x2 y2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=[x3 y3; x4 y4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere (x1,y1) and (x2,y2) form a line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61303,"title":"Steering 101-Ackermann Steering Ratio","description":"In a turning vehicle, inner and outer wheels follow different radii. Ackermann steering geometry ensures both wheels roll without slipping.\r\nGiven wheelbase L, track width W, and outer wheel angle δo, compute the inner wheel angle δi \r\nusing:\r\n\r\nYouTube concept reference","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 140.883px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 70.4297px; transform-origin: 467.496px 70.4414px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a turning vehicle, inner and outer wheels follow different radii. Ackermann steering geometry ensures both wheels roll without slipping.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven wheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, track width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and outer wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, compute the inner wheel angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδi\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eusing:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"192\" height=\"18\" style=\"width: 192px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003ca target='_blank' href = \"https://youtu.be/i6uBwudwA5o?si=AkGgaHat1SAAMDjJ\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eYouTube concept reference\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function di = ackermannInnerAngle(L,W,do)\r\ndi = 0;\r\nend","test_suite":"%%\r\nL = 2.5; W = 1.5; do = 20*pi/180;\r\ndi_expected = atan(1 / (1/tan(do) - W/L));\r\nassert(abs(ackermannInnerAngle(L,W,do) - di_expected) \u003c 1e-6)\r\n\r\n%%\r\nL = 3.0; W = 1.6; do = 15*pi/180;\r\ndi_expected = atan(1 / (1/tan(do) - W/L));\r\nassert(abs(ackermannInnerAngle(L,W,do) - di_expected) \u003c 1e-6)\r\n\r\n%%\r\nL = 2.8; W = 1.4; do = 25*pi/180;\r\ndi_expected = atan(1 / (1/tan(do) - W/L));\r\nassert(abs(ackermannInnerAngle(L,W,do) - di_expected) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:12:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:11:44.000Z","updated_at":"2026-04-29T23:14:52.000Z","published_at":"2026-04-28T09:12:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a turning vehicle, inner and outer wheels follow different radii. Ackermann steering geometry ensures both wheels roll without slipping.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven wheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, track width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and outer wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the inner wheel angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδi\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eusing:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\delta i = atan( L / ( (L / tan(\\\\delta o)) - W ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://youtu.be/i6uBwudwA5o?si=AkGgaHat1SAAMDjJ\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eYouTube concept reference\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44060,"title":"Volume Pillar","description":"Calculate the volume of a pillar with radius l and heigth ar.","description_html":"\u003cp\u003eCalculate the volume of a pillar with radius l and heigth ar.\u003c/p\u003e","function_template":"function y = Pillar_Size(l,ar)\r\n  y = x;\r\nend","test_suite":"%%\r\nl = 1;\r\nar = 2;\r\ny_correct = pi*2;\r\nassert(isequal(Pillar_Size(l,ar),y_correct))\r\n\r\n%%\r\nl = 12;\r\nar = 25;\r\ny_correct = pi*3600;\r\nassert(isequal(Pillar_Size(l,ar),y_correct))\r\n\r\n%%\r\nl = 6;\r\nar = 2;\r\ny_correct = pi*72;\r\nassert(isequal(Pillar_Size(l,ar),y_correct))","published":true,"deleted":false,"likes_count":15,"comments_count":1,"created_by":99516,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2146,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-06T15:36:59.000Z","updated_at":"2026-04-30T17:09:36.000Z","published_at":"2017-02-06T15:36:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the volume of a pillar with radius l and heigth ar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44276,"title":"Simple spirometer - find your lung capacity from the number and size of soap bubbles in one breath","description":"Assumed that each bubble has practically the same diameter d. Given total number n of bubbles. Find volume v of breath. ","description_html":"\u003cp\u003eAssumed that each bubble has practically the same diameter d. Given total number n of bubbles. Find volume v of breath.\u003c/p\u003e","function_template":"function v = spiro(n,d)\r\n  v=n/d;\r\nend","test_suite":"%%\r\nn=10;\r\nd=6;\r\nassert(spiro(n,d)\u003c365*pi)\r\n\r\n%%\r\nn=10;\r\nd=6;\r\nassert(spiro(n,d)\u003e355*pi)\r\n\r\n%%\r\nn=125;\r\nd=1;\r\nassert(spiro(n,d)\u003c25*pi)\r\n\r\n%%\r\nn=120;\r\nd=1;\r\nassert(spiro(n,d)\u003e19*pi)\r\n\r\n%%\r\nn=12;\r\nd=1;\r\nassert(spiro(n,d)\u003c3*pi)\r\n\r\n%%\r\nn=11;\r\nd=1;\r\nassert(spiro(n,d)\u003epi)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2017-08-08T14:35:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-06T18:54:26.000Z","updated_at":"2026-04-03T06:52:40.000Z","published_at":"2017-08-06T18:54:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumed that each bubble has practically the same diameter d. Given total number n of bubbles. Find volume v of breath.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2377,"title":"Area of a disk","description":"Find the area of a disk or circle. \r\n\r\nx= radius of the disk.","description_html":"\u003cp\u003eFind the area of a disk or circle.\u003c/p\u003e\u003cp\u003ex= radius of the disk.\u003c/p\u003e","function_template":"function y = crcl_area(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 12.57;\r\nassert(isequal(crcl_area(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 452.39;\r\nassert(abs(y_correct-crcl_area(x)) \u003c= 0.01)","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":377,"test_suite_updated_at":"2014-06-20T05:28:55.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2014-06-18T17:24:29.000Z","updated_at":"2026-04-30T06:34:22.000Z","published_at":"2014-06-18T17:25:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a disk or circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex= radius of the disk.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61306,"title":"Tire Slip Angle Calculation","description":"Slip angle represents the angle between the direction a tire is pointing and the direction it is moving.\r\nGiven Lateral velocity vy and Longitudinal velocity vx, compute slip angle α.\r\nEquation:\r\nalpha_angle = atan(vy / vx)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSlip angle represents the angle between the direction a tire is pointing and the direction it is moving.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Lateral velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evy \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLongitudinal velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evx, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecompute slip angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eα\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ealpha_angle = atan(vy / vx)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function alpha = slipAngle(vy,vx)\r\nalpha = vy;\r\nend","test_suite":"%%\r\nvy = 2; vx = 10;\r\nalpha_expected = 0.1974;\r\nassert(abs(slipAngle(vy,vx) - alpha_expected) \u003c 1e-4)\r\n\r\n%%\r\nvy = 1; vx = 5;\r\nalpha_expected = 0.1974;\r\nassert(abs(slipAngle(vy,vx) - alpha_expected) \u003c 1e-4)\r\n\r\n%%\r\nvy = 3; vx = 15;\r\nalpha_expected = 0.1974;\r\nassert(abs(slipAngle(vy,vx) - alpha_expected) \u003c 1e-4)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:23:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:23:12.000Z","updated_at":"2026-04-29T17:22:32.000Z","published_at":"2026-04-28T09:23:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSlip angle represents the angle between the direction a tire is pointing and the direction it is moving.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Lateral velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evy \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eLongitudinal velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evx, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ecompute slip angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eα\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ealpha_angle = atan(vy / vx)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":223,"title":"Which quadrant?","description":"Given a complex number, output quadrant 'I' 'II' 'III' or 'IV'\r\n\r\n        |              \r\n   II   |   I          \r\n        |              \r\n -------+------- real\r\n        |              \r\n   III  |   IV          \r\n        |\r\n      imag\r\n              \r\n","description_html":"\u003cp\u003eGiven a complex number, output quadrant 'I' 'II' 'III' or 'IV'\u003c/p\u003e\u003cpre\u003e        |              \r\n   II   |   I          \r\n        |              \r\n -------+------- real\r\n        |              \r\n   III  |   IV          \r\n        |\r\n      imag\u003c/pre\u003e","function_template":"function y = your_fcn_name(x)\r\n y='IV';\r\nend\r\nend","test_suite":"%%\r\nx = 1+1i;\r\ny_correct = 'I';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = -1-1i;\r\ny_correct = 'III';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 1-1i;\r\ny_correct = 'IV';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = -1+1i;\r\ny_correct = 'II';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":368,"test_suite_updated_at":"2012-02-02T03:13:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-02T03:13:00.000Z","updated_at":"2026-04-27T23:04:05.000Z","published_at":"2012-02-02T03:13:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a complex number, output quadrant 'I' 'II' 'III' or 'IV'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[        |              \\n   II   |   I          \\n        |              \\n -------+------- real\\n        |              \\n   III  |   IV          \\n        |\\n      imag]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44618,"title":"surface areas of a cylinder","description":"There are 3 inputs: option, radius and height. If option= '1', compute the lateral surface area of the cylinder, for option 2 calculate the total surface area of the cylinder. For any other option, compute the total area of both flat sides of the cylinder.","description_html":"\u003cp\u003eThere are 3 inputs: option, radius and height. If option= '1', compute the lateral surface area of the cylinder, for option 2 calculate the total surface area of the cylinder. For any other option, compute the total area of both flat sides of the cylinder.\u003c/p\u003e","function_template":"function y = surface_area_cyl(optn,r,h)\r\n  y = r*h;\r\nend","test_suite":"%%\r\noptn=1;\r\nr=3;\r\nh=6;\r\ny_correct = 36*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=5;\r\nr=3;\r\nh=6;\r\ny_correct = 18*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=2;\r\nr=2;\r\nh=2;\r\ny_correct = 16*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=0;\r\nr=5;\r\nh=10;\r\ny_correct = 50*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=1;\r\nr=5;\r\nh=10;\r\ny_correct = 100*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=2;\r\nr=5;\r\nh=10;\r\ny_correct = 150*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=42;\r\nr=3;\r\nh=7;\r\ny_correct = 18*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=2;\r\nr=3\r\nh=7;\r\ny_correct = 60*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n\r\n%%\r\noptn=1;\r\nr=3;\r\nh=7;\r\ny_correct = 42*pi;\r\nassert(isequal(surface_area_cyl(optn,r,h),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":53,"test_suite_updated_at":"2018-07-16T16:54:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-04-20T05:49:29.000Z","updated_at":"2026-04-03T06:59:13.000Z","published_at":"2018-04-20T05:49:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are 3 inputs: option, radius and height. If option= '1', compute the lateral surface area of the cylinder, for option 2 calculate the total surface area of the cylinder. For any other option, compute the total area of both flat sides of the cylinder.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45220,"title":"Find triangles from edge","description":"First input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\r\ne = [2, 4]\r\nand T a tetrahedron\r\nT = [1, 2, 3;...\r\n     1, 3, 4;...\r\n     1, 2, 4;...\r\n     2, 3, 4]\r\nthen the output of the function is\r\nS = [1, 2, 4;...\r\n     2, 3, 4]\r\nsince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\r\nConditions :\r\nIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\r\nEdges are symmetric : [e1, e2] is the same edge as [e2, e1]\r\nOrder of rows / edges in the output doesn't matter.\r\nTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u003c t2 \u003c t3.\r\nEvery indices are positive, distinct integers.\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 286.1px; transform-origin: 408px 286.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.5px 8px; transform-origin: 374.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8.5px; tab-size: 4; transform-origin: 38.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2, 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.4583px 8px; transform-origin: 61.4583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand T a tetrahedron\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eT = [1, 2, 3;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e     1, 3, 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003e     1, 2, 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.5667px 8px; transform-origin: 99.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the output of the function is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 20.4333px; transform-origin: 405px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 8.5px; transform-origin: 50.05px 8.5px; \"\u003eS = [1, 2, 4;\u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 11.55px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 11.55px 8.5px; \"\u003e...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2, 3, 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.567px 8px; transform-origin: 197.567px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8167px 8px; transform-origin: 40.8167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConditions :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 51.0833px; transform-origin: 392px 51.0833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 302.95px 8px; transform-origin: 302.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.6167px 8px; transform-origin: 69.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEdges are symmetric :\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 118.233px 8px; transform-origin: 118.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[e1, e2] is the same edge as [e2, e1]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 167.692px 8px; transform-origin: 167.692px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOrder of rows / edges in the output doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 330.342px 8px; transform-origin: 330.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 17.8917px 8px; transform-origin: 17.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 124.817px 8px; transform-origin: 124.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eindices are positive, distinct integers.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function S = find_triangles_from_edge(T,e)\r\n  S = [];\r\nend","test_suite":"%% Tetrahedron\r\nT = [1, 2, 3;...\r\n     1, 3, 4;...\r\n     1, 2, 4;...\r\n     2, 3, 4];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n     2, 3, 4];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Filled octahedron (two pyramids stuck together via their square bases)\r\nT = [1, 2, 3;...\r\n     1, 3, 4;...\r\n     1, 4, 5;...\r\n     1, 2, 5;...\r\n     2, 3, 6;...\r\n     3, 4, 6;...\r\n     4, 5, 6;...\r\n     2, 5, 6;...\r\n     2, 3, 4;...\r\n     2, 4, 5;...\r\n     1, 2, 4;...\r\n     2, 4, 6];\r\n\r\ne = [2, 4];\r\n\r\nS = [1, 2, 4;...\r\n     2, 3, 4;...\r\n     2, 4, 5;...\r\n     2, 4, 6];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Triangulated cube\r\nT = [1, 2, 4;...\r\n     2, 3, 4;...\r\n     5, 6, 8;...\r\n     6, 7, 8;...\r\n     1, 2, 5;...\r\n     2, 5, 6;...\r\n     2, 3, 6;...\r\n     3, 6, 7;...\r\n     3, 4, 7;...\r\n     4, 7, 8;...\r\n     1, 4, 8;...\r\n     1, 5, 8];\r\n\r\ne = [3, 7];\r\n\r\nS = [3, 4, 7;...\r\n     3, 6, 7];\r\n\r\nassert(isequal(sortrows(find_triangles_from_edge(T,e)),S))\r\n\r\n%% Empty set test\r\nT = [2, 3, 5;...\r\n     3, 5, 7;...\r\n     5, 7, 11;...\r\n     7, 11, 13];\r\n\r\ne = [6, 8];\r\n\r\nassert(isempty(find_triangles_from_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_triangles_from_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:51:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2025-07-09T05:48:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-03T18:46:56.000Z","updated_at":"2026-04-17T18:45:00.000Z","published_at":"2019-12-03T20:30:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst input is T, a Triplet list of indices -whom each row actually contains the three indices of a triangle vertices-. size(T) = [nb_triangles, 3]. Second input is e = [e1, e2], a row vector, couple of indices. Output S is the triplet list of indices which Share the edge e. For instance, if\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[e = [2, 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand T a tetrahedron\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [1, 2, 3;...\\n     1, 3, 4;...\\n     1, 2, 4;...\\n     2, 3, 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen the output of the function is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[S = [1, 2, 4;...\\n     2, 3, 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince both triangles [1, 2, 4] and [2, 3, 4] contain the edge [2, 4].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConditions :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the edge is not part of any triangle in the list, the function must of course return the empty set, [].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEdges are symmetric :\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[e1, e2] is the same edge as [e2, e1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOrder of rows / edges in the output doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTriangle indices are assumed always to be sorted in ascending order, T = [t1, t2, t3] with t1 \u0026lt; t2 \u0026lt; t3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eindices are positive, distinct integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45358,"title":"Do they touch?","description":"The center and radius of two circles are given.\r\n\r\nDetermine whether they touch.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 25.5px; vertical-align: baseline; perspective-origin: 332px 25.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe center and radius of two circles are given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine whether they touch at one point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = touch(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx1=[0,0];\r\nx2=[5,5];\r\nr1=3;\r\nr2=2;\r\nassert(isequal(touch(x1,x2,r1,r2),0))\r\n\r\n%%\r\nx1=[0,0];\r\nx2=[3,4];\r\nr1=3;\r\nr2=2;\r\nassert(isequal(touch(x1,x2,r1,r2),1))\r\n\r\n%%\r\nx1=[2,1];\r\nx2=[3,4];\r\nr1=4;\r\nr2=2;\r\nassert(isequal(touch(x1,x2,r1,r2),0))\r\n\r\n%%\r\nx1=[-1,0];\r\nx2=[3,-3];\r\nr1=3;\r\nr2=8;\r\nassert(isequal(touch(x1,x2,r1,r2),1))\r\n\r\n%%\r\nx1=[-5,-5];\r\nx2=[5,5];\r\nr1=5;\r\nr2=5;\r\nassert(isequal(touch(x1,x2,r1,r2),0))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2020-02-26T14:39:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-26T14:25:46.000Z","updated_at":"2026-02-24T05:33:32.000Z","published_at":"2020-02-26T14:39:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center and radius of two circles are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine whether they touch at one point.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1141,"title":"Volume difference between Ellipsoid and Sphere ","description":"Given an ellipsoid of semi  principal axis (a,b,c) find the volume of the difference between this ellipsoid and  the sphere within, round the result toward zero using the \"floor\" function. ","description_html":"\u003cp\u003eGiven an ellipsoid of semi  principal axis (a,b,c) find the volume of the difference between this ellipsoid and  the sphere within, round the result toward zero using the \"floor\" function.\u003c/p\u003e","function_template":"function y = ellipsoid_sphere_diff(a,b,c)\r\n  y = x;\r\nend","test_suite":"%%\r\na=2;b=2;c=8;\r\ny_correct = 100;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n%%\r\na=4;b=4;c=4;\r\ny_correct =0;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n%%\r\na=3;b=5;c=8;\r\ny_correct= 389;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n%%\r\na=4;b=6;c=8;\r\ny_correct=536;\r\nassert(isequal(ellipsoid_sphere_diff(a,b,c),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":5260,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":136,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":20,"created_at":"2012-12-25T23:34:50.000Z","updated_at":"2026-04-02T12:56:31.000Z","published_at":"2012-12-25T23:35:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an ellipsoid of semi principal axis (a,b,c) find the volume of the difference between this ellipsoid and the sphere within, round the result toward zero using the \\\"floor\\\" function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60166,"title":"Recursive triangle area","description":"Given triangle 1 with sides of length a, b, and c.  Triangle 2 is constructed within triangle 1 by bisecting each side.  Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides.  And so on. \r\nFind the area of triangle n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 71.9661px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 359.492px 35.9766px; transform-origin: 359.499px 35.9831px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 20.9896px; text-align: left; transform-origin: 336.497px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven triangle 1 with sides of length a, b, and c.  Triangle 2 is constructed within triangle 1 by bisecting each side.  Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides.  And so on. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 10.4948px; text-align: left; transform-origin: 336.497px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the area of triangle n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(a,b,c,n)\r\n  area = a+b+c+n;\r\nend","test_suite":"%%\r\na=1;b=1;c=sqrt(2);n=1;\r\ny_correct = 0.50;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=100;b=100;c=100;n=2;\r\ny_correct = 1082.53;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=13;b=33;c=44;n=4;\r\ny_correct = 2.0540;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3293343,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T18:08:43.000Z","updated_at":"2026-03-11T15:33:11.000Z","published_at":"2024-04-30T18:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven triangle 1 with sides of length a, b, and c.  Triangle 2 is constructed within triangle 1 by bisecting each side.  Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides.  And so on. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of triangle n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44282,"title":"Minimum possible M of the maximum side of a triangle of given area A.","description":"Suppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\r\n","description_html":"\u003cp\u003eSuppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\u003c/p\u003e","function_template":"function m = tri(a)\r\n  m = max(a/7);\r\nend","test_suite":"%%\r\na = 0.4331;\r\nm = 1.0001;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 43.31;\r\nm = 10.001;\r\nassert(tri(a)\u003cm*1.01)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003cm*1.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-10T11:39:30.000Z","updated_at":"2026-03-14T18:37:39.000Z","published_at":"2017-08-10T11:39:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose a triangle has area A. Suppose it has three sides S1, S2, and S3. Suppose M = max([S1 S2 S3]). What is the minimum possible value of M?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":49943,"title":"Splitting Hexagon - Problem the third","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 402px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 201px; transform-origin: 407px 201px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 279px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 139.5px; text-align: left; transform-origin: 384px 139.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the hexagon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 2 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5250;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[0 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[1 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3215;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.4981;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[4 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.8134;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 5 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5569;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T22:23:48.000Z","updated_at":"2025-12-27T03:32:18.000Z","published_at":"2021-01-22T22:24:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"273\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"307\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the 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Circle","description":"Consider a circle which has been divided into three concentric circles as depicted in the figure below\r\n\r\nThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 439.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 219.75px; transform-origin: 407px 219.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 315px 8px; transform-origin: 315px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 358.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.25px; text-align: left; transform-origin: 384px 179.25px; white-space: pre-wrap; margin-left: 4px; 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data-image-state=\"image-loaded\" width=\"359\" height=\"353\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = circle_split(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=circle_split(s);\r\ny_correct=[0.5774 0.8165];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[1 2 3];\r\ny=circle_split(s);\r\ny_correct=[0.4082 0.7071];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[3 2 1];\r\ny=circle_split(s);\r\ny_correct=[0.7071 0.9129];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[5 5 1];\r\ny=circle_split(s);\r\ny_correct=[0.6742 0.9535];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[4 4 0];\r\ny=circle_split(s);\r\ny_correct=[0.7071 1.0000];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":"2021-12-26T14:39:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T23:01:39.000Z","updated_at":"2026-04-28T12:38:25.000Z","published_at":"2021-01-22T23:03:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"353\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate 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of a spherical planet","description":"You just measured its surface area, that is the input.","description_html":"\u003cp\u003eYou just measured its surface area, that is the input.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 4*pi;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 400*pi;\r\ny_correct = 10;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 40000*pi;\r\ny_correct = 100;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = -4*pi;\r\ny_correct = 1i;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":19,"comments_count":9,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4430,"test_suite_updated_at":"2012-02-15T16:29:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-27T21:02:01.000Z","updated_at":"2026-04-30T16:57:47.000Z","published_at":"2012-02-15T16:45:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou just measured its surface area, that is the input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45218,"title":"Find a common edge","description":"First input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie e1 \u003c e2 ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\r\nFor example if inputs are\r\nT = [1 2 3 ;\r\n     1 3 4 ;\r\n     1 4 2 ;\r\n     2 3 4]\r\nand\r\ne = [2 3]\r\nthe output is the vector\r\nrow_idx = [1 4]\r\nsince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that edge [b a] is the same as edge [a b] so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\r\n\r\nSee also\r\nMesh generation\r\nMesh processing toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 500.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 250.3px; transform-origin: 408px 250.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.083px 8px; transform-origin: 377.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.5417px 8px; transform-origin: 23.5417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ee1 \u0026lt; e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.358px 8px; transform-origin: 247.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if inputs are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eT = [1 2 3 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1 3 4 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 46.2px 8.5px; tab-size: 4; transform-origin: 46.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     1 4 2 ;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8.5px; tab-size: 4; transform-origin: 42.35px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     2 3 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 34.65px 8.5px; tab-size: 4; transform-origin: 34.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ee = [2 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7833px 8px; transform-origin: 70.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe output is the vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 10.2167px; transform-origin: 405px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erow_idx = [1 4]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.667px 8px; transform-origin: 369.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.825px 8px; transform-origin: 117.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eedge [b a] is the same as edge [a b]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.725px 8px; transform-origin: 1.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/95796\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function row_idx = find_common_edge(T,e)\r\n  row_idx = e;\r\nend","test_suite":"%% Tetrahedron 1\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4];\r\n\r\ne = [2 3];\r\nrow_idx = [1 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Tetrahedron 2\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 2;...\r\n     2 3 4];\r\n\r\ne = [2 4];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Octahedron\r\nT = [1 2 3;...\r\n     1 3 4;...\r\n     1 4 5;...\r\n     1 5 2;...\r\n     6 3 2;...\r\n     6 4 3;...\r\n     6 5 4;...\r\n     6 2 5];\r\n\r\ne = [1 5];\r\nrow_idx = [3 4];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Triangulated cube\r\nT = [1 2 4;...\r\n    2 3 4;...\r\n    5 6 8;...\r\n    6 7 8;...\r\n    1 2 5;...\r\n    2 5 6;...\r\n    2 3 6;...\r\n    3 6 7;...\r\n    3 4 7;...\r\n    4 7 8;...\r\n    4 1 8;...\r\n    1 8 5];\r\n\r\ne = [6 7];\r\nrow_idx = [4 8];\r\n\r\nassert(isequal(find_common_edge(T,e),row_idx) || isequal(find_common_edge(T,e),row_idx'))\r\n\r\n%% Empty set test\r\nT = [2 3 5;...\r\n     3 5 7;...\r\n     5 7 11;...\r\n     7 11 13];\r\n\r\ne = [6 28];\r\n\r\nassert(isempty(find_common_edge(T,e)))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('find_common_edge.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:50:32.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2025-07-09T05:45:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-01T17:21:36.000Z","updated_at":"2026-04-17T18:42:43.000Z","published_at":"2019-12-01T18:01:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst input is T, a triplet list of indices. Second input is e = [e1 e2], a row vector, couple of indices (positive distinct integers always sorted in ascending order, ie\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ee1 \u0026lt; e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ). The goal of this function is to find and return the indices of the rows in the list which contain this particular edge. Output format can be either a column or a row vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if inputs are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [1 2 3 ;\\n     1 3 4 ;\\n     1 4 2 ;\\n     2 3 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[e = [2 3]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe output is the vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[row_idx = [1 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince [2 3] is contained in rows number 1 and 4 of T. With the same input T, but with e = [2 4] this time, the output is the vector row_idx = [3 4], since [2 4] is contained in rows number 3 and 4 of T (Note that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eedge [b a] is the same as edge [a b]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e so must be the corresponding outputs). If the edge is not in the list, the function must of course return the empty set.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/95796\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/77004-mesh-processing-toolbox?s_tid=srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing toolbox\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1443,"title":"Edges of a n-dimensional Hypercube","description":"Return the number of edges on an \u003chttp://en.wikipedia.org/wiki/Hypercube _n_-dimensional hypercube\u003e (with an integer n \u0026ge; 0).\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eReturn the number of edges on an \u003ca href = \"http://en.wikipedia.org/wiki/Hypercube\"\u003e\u003ci\u003en\u003c/i\u003e-dimensional hypercube\u003c/a\u003e (with an integer n \u0026ge; 0).\u003c/p\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function E = hypercube_edges(n)\r\n  E = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('hypercube_edges.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nE_correct = 0;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 1;\r\nE_correct = 1;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 2;\r\nE_correct = 4;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 3;\r\nE_correct = 12;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 4;\r\nE_correct = 32;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 5;\r\nE_correct = 80;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 6;\r\nE_correct = 192;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 7;\r\nE_correct = 448;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 8;\r\nE_correct = 1024;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 9;\r\nE_correct = 2304;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 10;\r\nE_correct = 5120;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 11;\r\nE_correct = 11264;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 12;\r\nE_correct = 24576;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 13;\r\nE_correct = 53248;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 14;\r\nE_correct = 114688;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n\r\n%%\r\nn = 15;\r\nE_correct = 245760;\r\nassert(isequal(hypercube_edges(n),E_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2013-04-28T07:06:47.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-04-22T11:46:41.000Z","updated_at":"2026-04-27T13:36:56.000Z","published_at":"2013-04-22T11:47:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the number of edges on an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Hypercube\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-dimensional hypercube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (with an integer n ≥ 0).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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Their robot’s arm reaches over a storage bin that is L inches long.  How long must the arm be to reach the object? Round to 1 decimal place.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA High School is trying to build their robot to be able to reach the hanging object which is H inches from the ground.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheir robot’s arm reaches over a storage bin that is L inches long.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHow long must the arm be to reach the object? 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Round to 2 decimal places.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 173px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 86.5px; transform-origin: 407px 86.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe total area of all four equal sections of the game field is N ft².\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEach section has a rectangle of dimensions X ft x Y ft reserved for a hanging scoring rack.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere is also a scoring bin that takes up an area of 1ft x 1ft.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHow much driving area does the robot have in each section? Round to 2 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 101px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 50.5px; text-align: left; transform-origin: 384px 50.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = findArea(N,X,Y) % Do not edit this line.\r\n  % insert your code here\r\n  N = ?;\r\nend % Do not edit this line.\r\n\r\n","test_suite":"%%\r\nassert(isequal(findArea(576, 2, 2),139));\r\n%%\r\nassert(isequal(findArea(333, 4, 4),66.25));\r\n%%\r\nassert(isequal(findArea(128.5, 4, 4),15.13));","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":542228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":323,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-13T16:30:44.000Z","updated_at":"2026-04-30T21:23:21.000Z","published_at":"2022-09-13T16:30:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total area of all four equal sections of the game field is N ft².\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eEach section has a rectangle of dimensions X ft x Y ft reserved for a hanging scoring rack.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThere is also a scoring bin that takes up an area of 1ft x 1ft.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHow much driving area does the robot have in each section? Round to 2 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"95\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"145\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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a sequence of points forming a closed path (first and last points are coincident) return the perimeter value.\r\nFor example:\r\n\r\n xy = [ 0,0 ;\r\n        1,0 ;\r\n        1,1 ;\r\n        0,1 ;\r\n        0,0 ];\r\n\r\n L = 4","description_html":"\u003cp\u003eGiven a sequence of points forming a closed path (first and last points are coincident) return the perimeter value.\r\nFor example:\u003c/p\u003e\u003cpre\u003e xy = [ 0,0 ;\r\n        1,0 ;\r\n        1,1 ;\r\n        0,1 ;\r\n        0,0 ];\u003c/pre\u003e\u003cpre\u003e L = 4\u003c/pre\u003e","function_template":"function L = perimeter1(xy)\r\n\r\n  L=xy;\r\n\r\nend","test_suite":"%% Test case 1: Square\r\n\r\nxy=[0,0;\r\n    1,0;\r\n    1,1;\r\n    0,1;\r\n    0,0];\r\n\r\n\r\nerr=(abs(perimeter1(xy)-4)/(4))*100;\r\nassert(err\u003c.1)\r\n\r\n%% Test case 2 : Circle\r\n\r\nt=[0:pi/100:2*pi,0]';\r\nxy=[cos(t),sin(t)];\r\n\r\n\r\nerr=(abs(perimeter1(xy)-2*pi)/(2*pi))*100;\r\nassert(err\u003c.1)\r\n\r\n%% Test case 4 : Half-circle\r\n\r\nt=[0:pi/100:pi,0]';\r\nxy=[cos(t),sin(t)];\r\n\r\nerr=(abs(perimeter1(xy)-(pi+2))/(2+pi))*100;\r\nassert(err\u003c.1)\r\n\r\n%% Test case 4 : Hexagon\r\n\r\nside=rand;\r\nx=side*[-1 -0.5 0.5 1 0.5 -0.5 -1];\r\ny=side*sqrt(3)*[0 -0.5 -0.5 0 0.5 0.5 0];\r\nxy=[x',y'];\r\nerr=(abs(perimeter1(xy)-(6*side))/(6*side))*100;\r\nassert(err\u003c.1)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":10742,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":157,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":20,"created_at":"2013-03-25T10:56:31.000Z","updated_at":"2026-04-07T18:48:49.000Z","published_at":"2013-03-25T10:57:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sequence of points forming a closed path (first and last points are coincident) return the perimeter value. For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ xy = [ 0,0 ;\\n        1,0 ;\\n        1,1 ;\\n        0,1 ;\\n        0,0 ];\\n\\n L = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":132,"title":"given 3 sides, find area of this triangle","description":"1:3 -\u003e 0; 3:5 -\u003e 6 ","description_html":"\u003cp\u003e1:3 -\u003e 0; 3:5 -\u003e 6\u003c/p\u003e","function_template":"function y = your_fcn_name(a,b,c)\r\n  y = x;\r\nend","test_suite":"%%\r\na=1; b=2; c=3;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(a,b,c),y_correct))\r\n%%\r\na=3; b=4; c=5;\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(a,b,c),y_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":821,"test_suite_updated_at":"2012-01-28T04:51:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-28T04:51:58.000Z","updated_at":"2026-04-23T21:15:08.000Z","published_at":"2012-01-28T06:11:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1:3 -\u003e 0; 3:5 -\u003e 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60980,"title":"Mesh the tetrahedron","description":"Problem statement\r\n\r\nAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\r\nA triangulated mesh -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, T. You will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles [1, 2, 3] and [3, 2, 1] are distinct).\r\nOn the other hand [1, 2, 3], [2, 3, 1] and [3, 1, 2] are one same unique triangle.\r\nThe row order of the triangles in the list doesn't matter.\r\n       \r\nEdit / update\r\nTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\r\n\r\nExample\r\nThe first triangle (X \u003e 0 and Y \u003e 0) here can be [1, 2, 4] if counterclockwise oriented (normals outward).\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1194.73px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 597.367px; transform-origin: 408px 597.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.592px 8px; transform-origin: 374.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.542px 8px; transform-origin: 157.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.533px 8px; transform-origin: 206.533px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 328.017px 8px; transform-origin: 328.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.51667px 8px; transform-origin: 7.51667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.4667px 8px; transform-origin: 49.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 2, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.0583px 8px; transform-origin: 40.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are distinct).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3417px 8px; transform-origin: 58.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOn the other hand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[2, 3, 1]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[3, 1, 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5333px 8px; transform-origin: 94.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are one same unique triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.5917px 8px; transform-origin: 13.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e       \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.9833px 8px; transform-origin: 41.9833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEdit / update\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 351.75px 8px; transform-origin: 351.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 8px; transform-origin: 52.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.2917px 8px; transform-origin: 53.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 4]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.208px 8px; transform-origin: 148.208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented (normals outward).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_tetrahedron()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct = [1 2 4;\r\n             2 3 4;\r\n             3 1 4;\r\n             1 3 2];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_tetrahedron(),2)),sortrows(sort(T_correct,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_tetrahedron.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:43:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2025-07-23T16:17:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T11:03:01.000Z","updated_at":"2026-04-21T19:49:47.000Z","published_at":"2025-07-23T11:11:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five well known platonic solids.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this tetrahedron. To do so, you will list the triangles/rows in a matrix of triangles, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eYou will also be careful to always keep the triangles / faces coherently / consistently oriented (all clockwise or all counterclockwise : triangles \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 2, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are distinct).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2, 3, 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are one same unique triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEdit / update\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangles orientation not taken into account anymore, because of too many possible cases to check in the tests (!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(X \u0026gt; 0 and Y \u0026gt; 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented (normals outward).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"378\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"504\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Segment Area","description":"Let us consider a circle with radius . If we draw an angle  (in radians) from the center of the circle, the two radii forming that angle intersect the circle at  and . We call  the area delimited by the chord and the arc  (the so-called Circular Segment, blu in the figure). \r\n\r\nFor a given radius  and area , compute the angle  (rounded to 6 significant digits).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 276.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 138.31px; transform-origin: 406.996px 138.31px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 62.7273px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 31.3636px; text-align: left; transform-origin: 383.999px 31.3636px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLet us consider a circle with radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35.5\" height=\"17.5\" style=\"width: 35.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If we draw an angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59.5\" height=\"17.5\" style=\"width: 59.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (in radians) from the center of the circle, the two radii forming that angle intersect the circle at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. We call \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"17.5\" style=\"width: 36.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the area delimited by the chord and the arc \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23\" height=\"17.5\" style=\"width: 23px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (the so-called Circular Segment, blu in the figure). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 175px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 87.5px; text-align: left; transform-origin: 383.999px 87.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"161\" height=\"175\" style=\"vertical-align: middle;width: 161px;height: 175px\" 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8da6ePEq0XC3bpCeHiIl3tR0lWgYADIzpdzuR98yFgJpTc3xpKWlWSyW0tLSVatW6agwU+OQqdf09DRhP4A44/ApUxZkZo774IP/m5ubG7JKxO/3z58/n+M4l8slJs9y9uyNJ8uAAb1D9oravdtNXgwefMfPfx55/1rx6DioJlkHjQTSQRijMFNfxBaHt7Ze/ec//x8JsLds+STwsUuK5MV7CLJNJ3SxNWdt7bmPPz4KAP369XzsMXrgwN4hThErupSx3+9funSpw+HQTiAdhFELM/VFYBzO894wDUl37fqfXbvey8jI+PLLL4njjaFf/AcfHCSXCFro2tJy/Ysv6r/7jgOArKyB8+Zl9ewpcRSsPxnzPM8wDMuyqmekw5MIhZm6g8Thzc3Xjh+/EBSHnzpVu26dBQAqKir69esXQ7/4v/2t+soVHwBkZ5uGDu3n97dfuHDlwoWrZ8+2dO+ePG4c9fOfUyHHzPGjMxkLg2FV+g9GRWIWZuoLEofzvPfMmZbz56/U1BwvK3uS9MemKOrEiRPiUxuXL19//fV9Yd5w5529TKbe48cPysoaKIHpt6MnGZMBpzYHwyHBwkzdcepUw6hRI3w+38MPP7xhwwbxrvj48QsORy0A9OiR8vTTE9LSUlNTk1tb27ze1gsXrn777dkffrhItDZsWL/HHx+XkhJ1GVkYpDyXrBQXFxMNsyyrCw0DQEFBAcuywh7liMbx+/1PPfUvPp/vqaee+vjjj/Py8rxesXWjZ8+2kBeDBvUZOLB3r16pKSlJvXunmkxpWVkDzeac+fOzyBtOnbq0bdsJaS3XgYz9fj8ZZzIMc/r0aR0NNRcvXgwAmzdvVtsQRBRLly51Op02m+3tt9+22WxOp3PUqFE8z4v5W467Mds0aFDfkG+g6Yx7772LvGbZc9IGwVqXMVlWUlRUZDab1WoCHDMmk4lhmLKyMr/fr7YtSASKi4sdDofVaiW5jGXLlrlcLtKwze12R/xzYdJ40KA+Xb1HqOtqbW1rbr4qgdE30bSMhaVhVqu1vLxcXxomrFixguO4mpoatQ1BwlFdXU3CvRdffFE4OG3aNJfLBQAjRoyorq4O8+fXrvkvXbpGXnfljQGgd2/pGwYQtCtjnucnTpxINKzf1UJCYabahiBdUltbS9IuncO9adOmsSxLUVRubm4YJQsD49TU5Lvu6rIfwOXL14XXaWnBu/PGg0ZlTFqlsCxbUVGhXw1DQGGm+GQJoiQ8z8+ePZukTkOGeyaTKaKShYExRfXp1vVGYUL9yaBBfbt3D72zZ2xoUcZEw6SW1QDFjIsWLQKA3bt3q20IEozf72cYhuO4TZs2hUmdRlSymIGx291MligCQJidPWNDczIO1LBeJpbCM2XKFIqiXn/9dbUNQYLJy8tjWdZut0e804iSGYbJzc1ds2ZN0G8jpqkvXLjy0UdHbp4q7f77B8dneDDakrHxNAwAKSkphYWFTqdT5NQFogzFxcUk8yKyHNBkMlVVVTEMs3z58kAl+3xt589fIa87e2Ovt3XPnpP/+McBUvg5cGDvxx+nk5K63qE3JjRUxWVIDROwMFNrxLyVqTB7smePKzV1eEtLa31905kzN1JcEyYM6tkzJTk5yeNpvXTp2uXL1y9cuEoklpqa/MADQ3Jzh0k7KiZoRcYG1jABCzO1A3mqxtwvXlDyk0+WDhsWuqFXUlK37t2Tu3dPvvPOXunpaZmZ/e+5Z0DIRcjS0KEBPB4PRVEA4HK51LZFLmw2GwCwLKu2IYlOY2MjRVEURTU2NsZ8Eq3dseqPjQN7LBjSDxOwMFML+P1+EvRt3749nqretLQ0MfPJyqHuU8Tn8zEMAwB2u11dSxSAYRiKonw+n9qGJCjCzVZRUSHJCYljBw0EWSrLmPxbrVarumYoQ0VFBWgmDEtArFar5DebJCF6/KgpYzn+rVrG4/EAgMViUduQRMRutwMAwzCSn5nUXVMU5fF4JD+5SFSTMUn5yPFv1TIWiwUAVPy+ExOiNIZhZBrRyH3+iKgjY9U/tlqQDy7V2AwRgzJxr7puSQUZ19fXqx6EqIXP56MoKtFiEBURZobq6+vlvpaKg0SlZSwk99RNCagI+bIT9uMriZCaViatKHkmXDyKyljhf6s2YVkWAGw2m9qGGB+SiVDSPZJoSxnnH4iiMib/VryDaZqmKEptKwwOGayazWaFrysMxZUcMyonY5LxV/7fqkGwMFNu1M2hKn91hWRM0lo0TSdaajokjY2NCTVhrjDk36tuSQZ5Uiv2FSuxwolsaMRxHO6EIjBr1iyn0+nz+fTYJ1DLeL3eUaNGaeFmI1+xMisFlFgakZeXR1Y+oIYFVqxYAQDYMVNaApfZqH6zffLJJ2TthBLtIuR292RIjAFkEKQwEzMF0mI2m0FLOVQyllRgkCyvjHFIHAYszJQWMiGvtZJ1ZQbJMspYmEPDUoeQYGGmhGi5vJfUSsg6MSFjiots1l5RUWGAJrVyQDJ/6enp2NknTtxu94gRI6LdylQxSNYNAGQ0T6bHA6lVwrFfeLAwM340suI3PCRYkE8OssiY1KMn5uKHqMDCzDjRUXkvSYXINIaSRcYkYaj9/6wWwMLMeCB3mi46QJFUkUy+TXoZyx0/GAwszIwZ3XWPkW+kKbGMZX3kGBIszIwN0thMm6npMMgUWkssY1kHAEaFjO70dTuqC3FremwzKvg5aS2XUsak2APD6WjBjplRoYvUdBjIqFPaMhXJZOzz+WiaBixLih4szBSPcJvp+qlHMnMSthaQTMakdloXOUMNgoWZIlGrS460kAe3hEXK0shYMEuSsyUgWJgpBt2lpsMgrduTRsYkSMBZk5ghmQ98DoZBvn7xqkBGB1LN6UggY8xsSQIWZoaBRCsGWypH8u2S5LokkDFmtiSBPA2xMLMzek9Nh0GqXFe8MiaTJXjzSQIWZnZGWO5qyCEbKf6JP5KNS8YyzWUnLFiYGYSKDdwVgwym4pw/i0vGOMkkLSThb4xMrCQYKTXdFWQ5YJzZzdhljMlVOVCmMPPs2bNffvllc3OzrFeJk8RpbE4+aTwOOXYZkwhQ18U0GkSZwsxf/epXAHDkyBFZrxIPWm7KIznxD05jlDHWe8iEz+eT2wXt2rULAHr06KFZhcTQL57n+d///ve//e1vDx48KKttMhHn+DRGGUsyLkdCIndh5owZMwBgwoQJMp0/TmLbylTo9zZo0KDr16/LZp1cxOmQY5ExumJZka8ws6Wl5a9//Su53fPz8z0BXLlyRfLLxUBsTXmOHj0a2F7u8OHD8lkoH/E45FhkjK5YbuTIHb700kv9+/fvqrPi2LFjpb1cbMS2lanD4QCAESNGJCcnDxs27Nq1azKZJyvxOOSoNxDy+/1lZWU0TSuwM03CUlhYWFRUxPO8hDuYnDlz5pFHHtmzZ8/3338PAL///e8HDRok/DYjI0OqC8XMmjVrSktLLRbLSy+9FNUfchwHAHv27OnTp09TU1OPHj3kMVBeUlJSSkpKlixZUlNTE7W4otV9/MlxJCLyFWaOHz+efO9NTU2SnzweYkhN792795133uno6Pjv//7vYcOGyWmdQsQ8iRudjHGuWDHkKMy8fv16amoqAPzsZz+T9sxxIqSmo0rs3X///T179jx48OCHH344Y8YM+cxTktjcZHQ7Km7fvp3juJUrV0bn8ZHoKSgo4DiutrZWwnOyLEsmtCZMmCDhaeOE53myuoZlWfGbKmzZsuWrr766du3a7373u5EjR166dElOG5Vj3rx5APDyyy9H92dRiZ64CM3ONxoJOQoz33rrLfKlr1q1SsLTxkNsqen29vacnBzhHn700UdHjhxpmNuSpJCjmm+LQsa4xYHCSF6YWVBQQO77zz77TKpzxklsW5mWl5cDwEMPPfTwww+TT5ScnLxp0yaZjFQYMsSIah1yFDIm/3FcV6wYkhdmCvmtc+fOSXXOeIh5K9OZM2c+88wzPp/P4/GMHTuWfKgJEya0trbKYafyRKs1sTImMZ7WNo81NtIWZgr5rSFDhkhywjiJp2q6paVFeH3ixAlhPvz555+X1EbViDbyFStj8uDEpbAKI2Fh5v79+8m9/tvf/jb+s8UJmVGTKs9SWVmZlJQEAElJSZ9++mn8J9QCUU1ViMpUCyUfgXkFRAEWLVoEALt3747/VAcOHCAvVE9T8zz/i1/8gqIolmVTUqIuQOpMXl5ecXExALS3t+fn5xNXpndWrlzJcVx1dbWod4vROrZfVRGpJuqfeeYZ8o1//PHH8Z8tZmTqF9/e3j5//nzyAYcNG8ZxnIQnV4WoNiEQJWMy4DZMQl9fSNUxMzc3l9zlhw4dksSw2CDpdzk6xly+fDkrK4t8xgceeODq1auSX0JhxA+pIssYk1vqIlVh5siRI8kt/s0330hiWAzI3ZTn2LFjd9xxB/mYBmgbIj7RFVnG2OdNdSQpzCShLAA8+uijworcY8eObdiwIW4DRaHMVqZbtmzp1q0b+aQGaOIlckgVWcbYdVV1JHmSPvHEE0JC5M477xwzZky/fv0AYOHChVLZGQYltzIVFkh169ZN7zUhIr/6CDLGHuhaQJLCzJMnT44ZM0a4v++7775///d//+GHH6QyMgwK94tvb2+fM2cOAPTr10/L/cbEIHIX+wgyxh1JNIIkhZk+n+/IkSP79+9XshRPSE0rOS5rbm4ePXr0tm3bFLuifIgJhyPIGJclagSdbmWuYr94r9er8BVlgnz14R+C4co/amtrOY4T6ukRFZk9ezYAvPHGG2obEh2rVq1yOp1Wq1VoeacYvXv3VviKMjF9+nQA2Lx5c7g3hZE4RtSaQndbmRtsK1MVYRgmfFwdTsYYUWsKfdXSGXIrU7WIGFd3GVS73W6MqDXFtGnTKIp64YUX1DYkMjzPP/LIIxRFOZ1OSaqmE5zJkydD2Li6Sxlv3boVABYvXiyHWUhsFBYWsizL87zahoTD7/fTNM1x3L59+yTs7JnImEwmmqbLysq6ekOXMl67di1FUfg1aIqlS5cCwIYNG9Q2pEv8fn9eXh7HcS6XKzMzU21zjAPpzdbVEzy0jL1eL8uyhYWFchqGRE1mZiZN06+88orahnTJc889R1LT2MZcWubOnQtdP8FDy5gscJ05c6Z8ZiGxIUfHTKkg/eLNZnO0/eKRiGRmZlIUtWXLlpC/DS3jbdu2AcCUKVNktAuJCVIaHWEWUQ2qq6uXL1/OMMz777+vti3GZNGiRU6n0+/3h/hdyPw1RVE43adZlNnKPCpi2MoUiZYwlXwhJgPIVFNJSYm8zxYkVlasWOF0Orva6cfr9fI8v3fv3s6/6t+/f3Z2NgBIm3zyer2kahpT07JCyrl27NgR4nvvrGxSfBNVt2tESYI6Zno8HpfLZbFYiJcWCUVRFouloqIiTv8ZW794JDZomg5ZkRVCxqRlj/wmIbFDCjNLSkoCpUvTtNlsttvtFRUV9QGQP2lsbKyvr3e5XHa73WazBWneYrHEpkNiCS5lVQZSH925IDeEXMEQDVCMDSl1JE7VarW6XK4Yhso+n49l2UBJUxRls9nEl23H3C8eiQ3yvXd+4AbLmPQJkKPjGSIt6enpWVlZUp3N4/HY7Xah0Y/ZbI44qoqnXzwSG101kAiWMcmG4cBY+8i0/oxlWTKqIrdLV55Z6BevoxVXxoCm6c6zSMEyJkMdfL5qH1n7K9XX1wtittlsQfcDacojx0MEiUhIhQbLOKTWEW0id7dDlmVJmE3TtKBYTE2rS8iJpNuquEgp9YMPPih+3gJREbkLM3Nycg4ePGi321mWTU9Pr6ysBIClS5c6nU6bzYZV06owdepUAAiuCwjUNInT9LIwHVFsJ4D6+noSRZNNvAzQ/1nXdP7Sb5MxFn7oDsUKM30+3+9+9zsAmDlzJqZO1IVhmKAikNuC6pqaGpC6Ug+RlRUrVsDNL05Wjh49+uGHH2ZkZHz22WfY0ENdsrOzWZYNXCNxm4x37doVVUEfojqkY+bLL78s61V4np89ezZFUa5GwoAAABHnSURBVLW1tahh1SFLD3/66SfhyG0yZlmWlM4jeiElJcVisTidTq/XK9Ml/H4/wzAcx23atAlXPmgBkuU6cuSIcOSWjN1uN+AaYx1CtjLvakF5/OTl5bEsa7fbMTWtEcjDtK6uTjhyS8YNDQ1wMxWJ6AjSMfO1116T4+TFxcWkKU9+fr4c50diIC0tDW6fc7ol45MnTwIAmVdA9IVMHTMrKyuLiooYhsGmPFrDbDbv3LlT+PGWjElHWxz86BHSMTNMA9QYqK6unjNnDk3TVVVVEp4WkYSsrCyO44Qfb0txCQtcEH1BOmZKKGPsF69xRo0aBTfzWRAoY4fDIex/i+gOCQszhX7x27dvx+hMm5AcVktLC/nxhozJVDJJZCN6hHTMfPvtt+M8j9AvvqKiAvOdmqVv374AIDy1b8iYTCUPGDBALbOQOElLS2MYprS0NHQDVNGouJUpIp4hQ4YAwMWLF8mPt42N8emra+IvzCwvL8fUtC4gCQthzumGjMnPxFMjOiXOwszq6uolS5YwDIOpaV0QmJC+zRtjPkPXxFOYKaSmy8vLMTWtC8aMGeNwOMjrGzImkRipDkH0S2yFmaRfPG5lqi8Cv6kbMtb4lrmISGIozPT7/fPnz8etTHUHWf5AMpq3gmpcomgMoi3MxK1MdQ2ZY7ohY4fDgdGUMYiqMBO3MtUvw4cPF16H3hgV0S/iCzNxK1NdM3jwYLhZyHVLxllZWapZhEjKypUrIxZm8jyfm5uLqWm9Q77lWzImxdaIAZg3bx6ELcwUtjJlWRYHUwYgCQLWSSDGIHxhZmBqGjWsX0JMOCEGg9RyhSzMxH7xxiCwygNlbEzIpGLnwszi4mKHw2GxWJYtW6aCWYjUkNURt2QcmL9G9E7Iwszq6mqy8qGkpERF2xAJIashbsmY5K8Rw/D0009DQGGm2+0mqelPPvkEU9MGA4Nqw5KTkyMUZvI8/4tf/IKiKJZlsXLeeKCMjQwpzDx79mx+fj72izcwKGMjU1hYCAC5ublOpxP7xRuYJAhozIUYDJPJdO+999bV1WG/eGOTAtj0w9C4XC6O40aPHq22IYiMYMbS4JhMJhwPGx4cGyOI7kEZI4juQRkjiO65JePAXY8RBNERt2Tc3Nysoh0IgsQA2bAJg2oE0TFkwyaUMYLoksDmp0kAgN2JEUR3BC5BveWN49nCC0EQFbklY9w4AkF0x20pLoqiVDUGQZDoCJwhviHjGTNmHD58WCV7EASJmsAZ4ltBNcuyahiDIEjsDBkyBAQZ45YRCKIvtm7dCgCkrdoNGZMtIzDLhSA6Qkhp3Vb+EcMu9QiCqMLhw4dnzJhBXt+QMUlbNzQ0qGYUgiDREJjMus0bnzx5UnFjEASJGhI4z507l/x4Q8akHvPEiRMqWYUgSBQEpbFu88bHjh1T1hgEQWKBjH/JWBgCZWw2m3fu3KmOUQiCRAMZ/wobgNySsclk4jhOHaMQBIkGspBJ6Hl6S8ZkK03cshxBtM+RI0domhZ+vCXjnJwcwDknBNEDTqdzzJgxwo+3ZEwqQnDOCUE0DklTC7NNEDQ2hpuFmgiCaBaSwxo+fLhw5LYJJ4ZhcLkigmic2tpaABg8eLBw5DYZP/jggyzL+v1+pe1CEEQ0JE0d2ELvNhmTdU4//fSTslYhCBIFu3btYhgm8MhtMiZFIXv37lXUKARBROP3+1mWffDBBwMP3iZj0kkAW2QiiGYhwfKkSZMCD94m45SUFIZhdu3apaRZCIKIhwTL2dnZgQeDd40gWS7sH4Ag2oRMCQdtEREsY+Ks6+rqlLIKQZAo2Llzp9lsDjoYLOPJkycDwO7duxUyCkEQ0fA8z3GcsD5RIFjGJpOJoqgtW7YoZRiCIGLZv38/AEyfPj3oeIgdFRctWuR0OrEIBEG0xrZt2wBg9OjRQcdDyPjXv/41ABw9elQBsxAEEc/GjRsZhiG9qQMJIWMcHiOIBiED43nz5nX+VQgZk+Hx2rVr5TcMQRCxdDUwhpAyBoDCwkKcPUYQTbF+/XoINTCGrmQ8c+ZMAPjuu+9kNQtBEJH4/X6Hw2E2mzsPjKErGZO+XBs3bpTXNARBxEFSzo899ljI34aWMSmuLi0tldEuBEFEs3nzZriZfu5MaBkDwBNPPAE3+wwgCKIuZWVlNE0LHW2D6FLGs2bNgpvPAARBVIRMNRUUFHT1hi5lbDKZaJouKyuTxzAEQcSyYcMGAFi8eHFXb+hSxgBQUFDAcRzG1QiiLmvXrqUoqquIGsLLmKgf42oEURGe51mWLSwsDPOecDLGuBpBVIdE1AsWLAjznnAyBoyrEURt1q5dS9M02ZupKyLIGONqBFGR2tpalmXD5KgJEWRsMpkYhikrK8PlxwiiPMSDhslREyLIGABWrFjBcRx2vUUQhfH7/eGrPgQiy3j27NkA8MYbb0hjGoIg4qipqeE47tVXX434zsgyTklJsVgsDocD1y0iiJIQ30n8aHgiyxgAnn76aQB499134zQLQRCReL1eh8NhsVhCrkwMQpSMc3JyaJp+5ZVX4rYNQRBRlJSUwE0PGhFRMgaAlStXchxXXV0du10IgohDSG6Fny4WECtj0sgLE10IogDik1uEbh0dHSLfWlxcXFRUVF9fH7R/DIIg0jJu3DiWZX0+n5iBMYj3xgCwdOlSAHj//fdjNA1BEBG43W6WZa1Wq0gNQ1TeGABmzZrldDo9Hk9aWlpMFiIIEoH8/HyHwxGVyqLwxgDw8ssvAwDu8IQgMkHmmcxmc1SeMjpvDADjxo1rbGw8ffq0eI+PIIhIYstAReeNAeDNN9/kOA573yKI5Hi93qKiIoZhos0iR+2N/X7/0KFDAQAdMoJIC3HFLpdr2rRpUf1h1N44JSWlpKQEHTKCSAtxxTRNR6thiMEbAzpkBJGBmF0xxOCNAR0ygkhNPK4YYvPGgA4ZQSQlHlcMsXljQIeMINIRpyuGmL0xAPj9/okTJ+IcMoLECXHFLMuKXM/UmRi9MQCkpKSQOeS33nor5pMgSILD83xRUZHZbI5ZwxCPNyaQpRhYZY0gsUEqqONcOBi7NyasX78eAF588cU4z4MgCYjb7SadeuJc/BuvNwaJHicIkoBIFczG640BYPXq1QAQsbE9giCBlJeXsyxrs9niH5BK4I3hZqqtoqLiN7/5TfxnQxDDI23lhTQyxmoQBImKOOs9gpAgqAaAlJSUd955h+O4VatWSXJCBDEwbrebTDJJomGQyhsTSIsfzHUhSHhIZquxsTHi5kwikcYbE8rLy+FmK1wEQUIiZLak0jBIK2OTyWSz2ViWJXpGECQInueXLFlC0/Szzz4r4WmlDKrhZqG1tAEDghgGmQaeUnpjAEhJSSF9M/Pz86U9M4LoncrKSqfTabVaJU8eSeyNCWvWrFm+fLndbkcxIwiB53mapkGeSVlZZIyhNYIEQcLpeFYjhkHioJoghNYMw/j9fjkugSA6ory83Ol02mw2OTQMMskYADIzM+12O8uyuBoZSXBkyk4HIktQLSBrIIEg2keZAaZc3phQXl5OUdTs2bO9Xq+sF0IQbfLcc8+xLGu322VNEskrY5PJtGnTJo7j5s+fL+uFEESDVFZWlpaWms1muadskskmifIxbNiwpKSkdevWDRw48P7775f1WgiiHXieHz9+PEVRe/bsSUqS11/KOzYm+P3+vLw8HCQjiYMwJFZmpZC8DwlCSkqKMEjmeV6BKyKIughDYmVW+ykhYwgYJOfn5+NMMmJsysvLS0tLLRaLclWMHQpis9kAwGKxKHlRBFESl8sFAAzD+Hw+xS6qxNg4ENJGE8utEUMiFE6zLKtkGbLSMhbSXVJ1IUIQjUA60nEcp3wqV6GxsYCQ7srNzcV0F2IYiH/iOK6iokL56RilZQwAJpNp3759AEDTNCoZMQarVq0ia4nV6fGs2Cg8CFUyAQgiB1arFQDMZrNaBig9Ng6kvLx8yZIlDMNUVVVhd2tEp1RWVs6ZM0fd21j2Ysww5OTkkDrNEydOLFy4UC0zECRmqqurGYahKOrAgQMquiI1ZQwA06dPT0pKstlsSUlJ06dPV9ESBImW6urq3NxciqJYlu3bt6+KlqgZVBOEKSir1frSSy+pawyCiITn+fT0dKJh1TtVqZCpDiIlJaWqqophmKKiouLiYrXNQZDIqFXm0RXqyxhQyYiuIBrmOM7lcmlBw6ARGQMqGdEJgRrWThmiVmQMqGRE82hTw6ApGQMqGdEwmtUwaE3GgEpGNInb7dashkGDMgZUMqIxqqurR4wYAQAsy2pQw6CFeeOuEOaTLRZLSUkJVmsiqhBY46GRvHRntOiNCcQnW63W0tLSvLw8bP2DKE95ebn2NQyg3gon8ZDlIwzDNDY2qm0LkkDo6MbTgYw7OjrsdjsAUBSl/X8oYgB8Pp/FYgH9LKTV7tg4CDJEAQBtpgoRw+D1eufPn6+vpIx2x8ZBTJs2rb6+nnT/KS8vV9scxJjwPD9q1CiyUGf16tW60DCAHsbGgTQ2NjIMAwAWi0UX0Q6iI0hHGgBwuVxq2xIdOpNxR0eHz+czm82gk9wDohdIQouiqPr6erVtiRr9yZhAOteTmQC1bUH0TaBj8Hg8apsTC7oZGwexbNkyEgLRNL1mzRq1zUH0itvtHjp0qMPhsFqtVVVVaWlpalsUE2o/R+JCGCqbzWYcKiPRQiYyAaCiokJtW+JC3zLuCJjiwwAbEY8QSNM0bYAMi16DaoGUlJTVq1dXVFQABtiIOGpra0kgbbFYDhw4oOkqS5Go/RyRDCHAxgw20hU+n09Ijuo9kA7EODLuCPiSAMBut6ttDqIt6uvrSR884z3oDSVjgoG/LSQ2DP98N6CMOzo6fD4fmc036teGiEd4rNM0rcfSDjEYU8aEQLds1O8PCYPhnbCAkWXccfsXabPZcG45cWBZlqKoBBlbGVzGhPr6epLEpihKd1XvSLQ0NjaSOWGDpaPDkBAyJtjtdvJ4NpvNGGMbksDgy2Kx6LRAOgYSSMYdt6e+rFZr4nzNiUBFRQV5TBs4ldUViSVjQn19vRB02e12HDDrHZZlSS6TfKFqm6MCiShjgsvlSvDv3gAIT+QET2EmrowJwoCZpmnMfumIQAHj+CjRZdzR0eHz+VDMOiJQwGaz2fCTSWJAGd+gs5gTNkLTLEECTrQ8VhhQxrcRKGZMgGkHl8uFAg4DyjgEQWLGoZda+Hy+iooKkokkY2AMoUOCMg6HkM0mTgC7iyiGx+Ox2Wz4JBUJyjgygUMymqbtdjveUvIRGD/TNF1RUYHjmoigjMUS6B9IrR86ZwlpbGzEf2/MoIyjJtBdUBRls9lwwBYzHo+noqKCLFzBYCdmUMYx4vF47Ha7MHKmaRr1LB6fz+dyuUhLUyF9he43ZnSzo6Jm4Xm+rKysrKyM4zgAoGm6oKBg8eLFRui3KDVer3f37t3btm0rLS0lRywWy6JFi6ZMmaKbTc80CcpYMmprazdv3izomaKowsLCBQsWjB49OsHvUZ7nN2zYsGXLFqfTSY6geqUFZSw9brd769ata9euZVmWHGEY5oknnpg6dWpmZqaqpimH1+v97rvvNm7cuHHjRuG5tmjRIlSvHKCMZaRzDAkAZrN57ty5hpQ0z/PHjx/fsWPHRx99FPgImzdv3ty5c433ebUDylgh3G733r17t27d6nA4hIPkFh8/fvy9996rx7G01+utq6urra3dunXrzp07idcFAJqmFy5cOHPmTHS8yoAyVgEi6ZqaGiHgJJjN5qysrFGjRk2dOtVkMmlwdz+3293Q0HDy5Mkg3QKA2WyeOnXq9OnTR44cqUHLjQ3KWGW6cmgEMkE9d+7c/v37Z2dnA4AyoanX6+V5nij2xIkTx44dC2lbVlbWpEmTsrOzMWBWF5SxtvD7/T/99NORI0fq6ur27t17+PBhYZAZCE3TY8aMAYCpU6cOGDCAHMzJyenbt6/4a+3du1d4vXXrVvIiMOYXoChqxowZJpNpypQpOTk5FEXpcQhgYFDGOoDnea/XG+gbAaCze4wf4vyJXAFg6tSpoJT/R+IBZax7iAMXfmxpaamtrQ3z/uHDhw8ePFj4MS0tDV2r3kEZI4ju+f/xS/quYauqVwAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9091px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4545px; text-align: left; transform-origin: 383.999px 10.4545px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor a given radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, compute the angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e (rounded to 6 significant digits).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = area_segment(r,a)\r\n  t=;\r\nend","test_suite":"%%\r\nr = 1;\r\na = pi/2;\r\nt_correct = pi;\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n\r\n%%\r\nr = 1;\r\na = pi/4-1/2;\r\nt_correct = pi/2;\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n\r\n%%\r\nr = 2;\r\na = 4;\r\nt_correct = 2.55419595;\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n\r\n%%\r\nr = sqrt(2);\r\nt_correct = pi*rand();\r\na = t_correct-sin(t_correct);\r\nt_guest = area_segment(r,a);\r\nassert(isequal(round(abs(t_guest-t_correct),6),0))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-22T13:20:31.000Z","updated_at":"2026-04-14T12:49:23.000Z","published_at":"2021-08-22T13:32:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet us consider a circle with radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If we draw an angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et \\\\in [0,\\\\pi]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (in radians) from the center of the circle, the two radii forming that angle intersect the circle at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. We call \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\\\\ge0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the area delimited by the chord and the arc \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (the so-called Circular Segment, blu in the figure). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"175\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"161\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, compute the angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (rounded to 6 significant digits).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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