{"group":{"group":{"id":282,"name":"Basics on π","lockable":false,"created_at":"2019-02-22T13:59:38.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"π is also called as Archimedes' constant. The historically first exact formula for π, based on infinite series, was not available until a millennium later, when in the 14th century the Madhava-Leibniz series was discovered in Indian mathematics.","is_default":false,"created_by":232412,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":1080,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":433,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"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\u003eπ is also called as Archimedes' constant. The historically first exact formula for π, based on infinite series, was not available until a millennium later, when in the 14th century the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.m.wikipedia.org/wiki/Madhava_of_Sangamagrama\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMadhava\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e-Leibniz series was discovered in Indian mathematics.\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\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: normal; 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=\"display: block; min-width: 0px; padding-top: 0px; perspective-origin: 289.5px 31.5px; transform-origin: 289.5px 31.5px; \"\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; white-space: pre-wrap; perspective-origin: 266.5px 31.5px; transform-origin: 266.5px 31.5px; 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; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eπ is also called as Archimedes' constant. The historically first exact formula for π, based on infinite series, was not available until a millennium later, when in the 14th century the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = 'https://en.m.wikipedia.org/wiki/Madhava_of_Sangamagrama'\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMadhava\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-Leibniz series was discovered in Indian mathematics.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2019-05-08T20:20:15.000Z"},"current_player":null},"problems":[{"id":167,"title":"Pizza!","description":"Given a circular pizza with radius z and thickness a, return the pizza's volume. [ z is first input argument.]\r\nNon-scored bonus question: Why is the function interesting?","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 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: 102.5px 8px; transform-origin: 102.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a circular pizza with 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: 2px 8px; transform-origin: 2px 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: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ez\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: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and thickness\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: 2px 8px; transform-origin: 2px 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\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: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return the pizza's volume. [\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: 2px 8px; transform-origin: 2px 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: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ez\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: 74px 8px; transform-origin: 74px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is first input argument.]\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: 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: 190px 8px; transform-origin: 190px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNon-scored bonus question: Why is the function interesting?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pizza(z,a)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('pizza.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'if') || contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nz = 1;\r\na = 1;\r\nv_correct = pi;\r\nassert(isequal(pizza(z,a),v_correct))\r\n\r\n%%\r\nz = 2;\r\na = 1;\r\nv_correct = 4*pi;\r\nassert(isequal(pizza(z,a),v_correct))\r\n\r\n%%\r\nz = 1;\r\na = 2;\r\nv_correct = 2*pi;\r\nassert(isequal(pizza(z,a),v_correct))\r\n\r\n%%\r\nz = 2;\r\na = 2;\r\nv_correct = 8*pi;\r\nassert(isequal(pizza(z,a),v_correct))\r\n","published":true,"deleted":false,"likes_count":372,"comments_count":313,"created_by":39,"edited_by":223089,"edited_at":"2022-12-19T07:41:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":23780,"test_suite_updated_at":"2022-12-19T07:41:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-29T16:17:01.000Z","updated_at":"2026-04-03T16:00:06.000Z","published_at":"2012-01-29T16:21:23.000Z","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\u003eGiven a circular pizza with radius\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\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and thickness\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\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the pizza's volume. [\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\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is first input argument.]\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\u003eNon-scored bonus question: Why is the function interesting?\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":43298,"title":"Calculate area of sector","description":"A=function(r,seta)\r\n\r\nr is radius of sector, seta is angle of sector, and A is its area. Area of sector A is defined as 0.5*(r^2)*seta;","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 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=\"\"\u003eA=function(r,seta)\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: 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=\"\"\u003er(m) is radius of sector, seta (radian) is angle of sector, and A (m^2) is its area.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sectorarea(r,seta)\r\n  y =\r\nend","test_suite":"%%\r\nr=1\r\nseta=pi/2\r\ny_correct = 0.7854;\r\nassert(abs(sectorarea(r,seta)-y_correct)\u003c0.001)\r\n\r\n%%\r\nr=2\r\nseta=pi/2\r\ny_correct = pi;\r\nassert(abs(sectorarea(r,seta)-y_correct)\u003c0.001)\r\n\r\n%%\r\nr=sqrt(2);\r\nseta=pi/3\r\ny_correct = pi/3;\r\nassert(abs(sectorarea(r,seta)-y_correct)\u003c0.001)\r\n\r\n%%\r\nr= 6\r\nseta=pi/6;\r\ny_correct = 3*pi;\r\nassert(abs(sectorarea(r,seta)-y_correct)\u003c0.001)\r\n\r\n%%\r\nr= pi\r\nseta= pi\r\ny_correct = 0.5*pi^3;\r\nassert(abs(sectorarea(r,seta)-y_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":21,"comments_count":6,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3452,"test_suite_updated_at":"2021-02-21T07:46:40.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-10-10T09:02:12.000Z","updated_at":"2026-04-03T16:02:03.000Z","published_at":"2016-10-10T09:02:12.000Z","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=function(r,seta)\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(m) is radius of sector, seta (radian) is angle of sector, and A (m^2) is its area.\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":953,"title":"Pi Estimate 1","description":"Estimate Pi as described in the following link:\r\n\u003chttp://www.people.virginia.edu/~teh1m/cody/Pi_estimation1.pdf\u003e\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: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 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: 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: 222.5px 8px; transform-origin: 222.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEstimate Pi as described by the Leibniz formula (see the following link):\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: 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\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80\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: 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: 121px 8px; transform-origin: 121px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRound the result to six decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [estimate] = pi_est1(nMax)\r\nestimate = nMax;\r\nend","test_suite":"%%\r\nnMax = 10;\r\ny_correct = 3.041840000000000;\r\nassert(isequal(pi_est1(nMax),y_correct))\r\n%%\r\nnMax = 1000;\r\ny_correct = 3.140593000000000;\r\nassert(isequal(pi_est1(nMax),y_correct))\r\n%%\r\nnMax = 1e6;\r\ny_correct = 3.141592000000000;\r\nassert(isequal(pi_est1(nMax),y_correct))\r\n","published":true,"deleted":false,"likes_count":20,"comments_count":19,"created_by":2640,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1792,"test_suite_updated_at":"2020-10-03T14:08:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-09-20T21:16:13.000Z","updated_at":"2026-04-03T16:16:19.000Z","published_at":"2012-09-20T23:13:59.000Z","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\u003eEstimate Pi as described by the Leibniz formula (see the following link):\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://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80\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:r\u003e\u003cw:t\u003eRound the result to six 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":120,"title":"radius 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":4358,"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":"2026-04-03T16:21:17.000Z","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":44309,"title":"Pi Digit Probability","description":"Assume that the next digit of pi constant is determined by the historical digit distribution. What is the probability of next digit (N) being (n). \r\n\r\nFor example if we consider the first 100 digits of pi, we will see that the digit '3' is occured 12 times. So the probability of the being '3' the 101th digit will be 12/100 = 0.12.\r\n\r\nRound the results to four decimals.","description_html":"\u003cp\u003eAssume that the next digit of pi constant is determined by the historical digit distribution. What is the probability of next digit (N) being (n).\u003c/p\u003e\u003cp\u003eFor example if we consider the first 100 digits of pi, we will see that the digit '3' is occured 12 times. So the probability of the being '3' the 101th digit will be 12/100 = 0.12.\u003c/p\u003e\u003cp\u003eRound the results to four decimals.\u003c/p\u003e","function_template":"function y = pidigit(N,n)\r\n  y = x;\r\nend","test_suite":"%%\r\nN = 101;\r\nn = 3;\r\ny_correct = 0.1200;\r\nassert(abs(pidigit(N,n)-y_correct)\u003c0.0001)\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[101,201,202,203,1001]),regexp(fileread('pidigit.m'),'[\\d\\.\\+\\-\\*\\/]+','match')))) % modified from the comment of Alfonso on https://www.mathworks.com/matlabcentral/cody/problems/44343\r\n\r\n%%\r\nN = 201;\r\nn = 6;\r\ny_correct = 0.0750;\r\nassert(abs(pidigit(N,n)-y_correct)\u003c0.0001)\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[101,201,202,203,1001]),regexp(fileread('pidigit.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nN = 202;\r\nn = 6;\r\ny_correct = 0.0796;\r\nassert(abs(pidigit(N,n)-y_correct)\u003c0.0001)\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[101,201,202,203,1001]),regexp(fileread('pidigit.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nN = 203;\r\nn = 6;\r\ny_correct = 0.0792;\r\nassert(abs(pidigit(N,n)-y_correct)\u003c0.0001)\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[101,201,202,203,1001]),regexp(fileread('pidigit.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nN = 1001;\r\nn = 9;\r\ny_correct = 0.1050;\r\nassert(abs(pidigit(N,n)-y_correct)\u003c0.0001)\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[101,201,202,203,1001]),regexp(fileread('pidigit.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n","published":true,"deleted":false,"likes_count":18,"comments_count":27,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":852,"test_suite_updated_at":"2017-10-21T07:59:48.000Z","rescore_all_solutions":false,"group_id":34,"created_at":"2017-09-11T06:41:07.000Z","updated_at":"2026-04-02T15:18:00.000Z","published_at":"2017-10-16T01:45:06.000Z","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\u003eAssume that the next digit of pi constant is determined by the historical digit distribution. What is the probability of next digit (N) being (n).\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 we consider the first 100 digits of pi, we will see that the digit '3' is occured 12 times. So the probability of the being '3' the 101th digit will be 12/100 = 0.12.\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\u003eRound the results to four decimals.\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":2908,"title":"Approximation of Pi","description":"Pi (divided by 4) can be approximated by the following infinite series:\r\npi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\r\nFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\r\nAlso, try Problem 2909, a slightly harder variant of this problem.","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: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; 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: 215px 8px; transform-origin: 215px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePi (divided by 4) can be approximated by the following infinite series:\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: 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: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\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: 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: 360px 8px; transform-origin: 360px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\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: 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: 25.5px 8px; transform-origin: 25.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAlso, try\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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2909-approximation-of-pi-vector-inputs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 2909\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.5px 8px; transform-origin: 128.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a slightly harder variant of this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pi_approx(n)\r\n y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = -0.858407346410207;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 2;\r\ny_correct = 0.474925986923126;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps)) \r\n\r\n%%\r\nn = 4;\r\ny_correct = 0.246354558351698;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 7;\r\ny_correct = -0.142145830148691;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 10;\r\ny_correct = 0.099753034660390;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 14;\r\ny_correct = 0.071338035810608;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 17;\r\ny_correct = -0.058772861819756;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 20;\r\ny_correct = 0.049968846921953;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 25;\r\ny_correct = -0.039984031845239;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n\r\n%%\r\nn = 42;\r\ny_correct = 0.023806151830915;\r\nassert(abs(pi_approx(n)-y_correct)\u003c(100*eps))\r\n","published":true,"deleted":false,"likes_count":18,"comments_count":0,"created_by":26769,"edited_by":223089,"edited_at":"2022-09-05T17:21:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1405,"test_suite_updated_at":"2022-09-05T17:21:56.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:29:10.000Z","updated_at":"2026-04-01T21:08:22.000Z","published_at":"2015-02-01T03:29:10.000Z","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\u003ePi (divided by 4) can be approximated by the following infinite series:\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\u003epi/4 = 1 - 1/3 + 1/5 - 1/7 + ...\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 a given number of terms (n), return the difference between the actual value of pi and this approximation of the constant.\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\u003eAlso, try\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=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2909-approximation-of-pi-vector-inputs\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2909\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, a slightly harder variant of this problem.\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":44273,"title":"Given a square and a circle, please decide whether the square covers more area.","description":"You know the side of a square and the diameter of a circle, please decide whether the square covers more area.","description_html":"\u003cp\u003eYou know the side of a square and the diameter of a circle, please decide whether the square covers more area.\u003c/p\u003e","function_template":"function y = sqci(sq,ci)\r\n  y = (sq\u003eci);\r\nend","test_suite":"%%\r\nsq = 2;\r\nci = 1;\r\ny_correct = (sq\u003eci);\r\nassert(isequal(sqci(sq,ci),y_correct))\r\n\r\n%%\r\nsq = rand;\r\nci = rand;\r\ny_correct = (4*sq^2\u003epi*ci^2);\r\nassert(isequal(sqci(sq,ci),y_correct))\r\n\r\n%%\r\nsq = 0;\r\nci = 0;\r\ny_correct = (0\u003e0);\r\nassert(isequal(sqci(sq,ci),y_correct))\r\n\r\n%%\r\nsq = 100;\r\nci = 4;\r\ny_correct = (7\u003e3);\r\nassert(isequal(sqci(sq,ci),y_correct))\r\n\r\n%%\r\nsq = 21;\r\nci = 127;\r\ny_correct = (3\u003e7);\r\nassert(isequal(sqci(sq,ci),y_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":3,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1739,"test_suite_updated_at":"2017-08-06T18:26:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-02T14:15:00.000Z","updated_at":"2026-04-02T16:02:03.000Z","published_at":"2017-08-02T14:15:06.000Z","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 know the side of a square and the diameter of a circle, please decide whether the square covers more area.\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":44660,"title":"Perimeter of a semicircle","description":"Given the diameter d, find the perimeter of a semicircle","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: 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: 172.5px 8px; transform-origin: 172.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the diameter d, find the perimeter of a semicircle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = perm_semicircle(d)\r\n  d\r\nend","test_suite":"%%\r\nd = 20;\r\ny_correct = 51.4159265358979;\r\nassert(abs(perm_semicircle(d) - y_correct) \u003c 1e-10)\r\n\r\n%%\r\nd = 42;\r\ny_correct = 107.973445725386;\r\nassert(abs(perm_semicircle(d) - y_correct) \u003c 1e-10)\r\n\r\n%%\r\nd = 50;\r\ny_correct = 128.539816339745;\r\nassert(abs(perm_semicircle(d) - y_correct) \u003c 1e-10)\r\n\r\n%%\r\nd = 100;\r\ny_correct = 257.07963267949;\r\nassert(abs(perm_semicircle(d) - y_correct) \u003c 1e-10)\r\n\r\n%%\r\nd = 135;\r\ny_correct = 347.057504117311;\r\nassert(abs(perm_semicircle(d) - y_correct) \u003c 1e-10)","published":true,"deleted":false,"likes_count":10,"comments_count":3,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2177,"test_suite_updated_at":"2021-08-03T16:46:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-29T14:09:07.000Z","updated_at":"2026-04-02T15:56:27.000Z","published_at":"2018-05-29T14:09:07.000Z","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 diameter d, find the perimeter of a semicircle\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":43215,"title":"Convert radians to degrees","description":"Given input in radians, output to degrees","description_html":"\u003cp\u003eGiven input in radians, output to degrees\u003c/p\u003e","function_template":"function y = RAD2DEG(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = pi;\r\ny_correct = 180;\r\nassert(abs(RAD2DEG(x)-y_correct)\u003c0.01)\r\n%%\r\nx = -pi;\r\ny_correct = -180;\r\nassert(abs(RAD2DEG(x)-y_correct)\u003c0.01)\r\n%%\r\nx = pi/2;\r\ny_correct = 90;\r\nassert(abs(RAD2DEG(x)-y_correct)\u003c0.01)\r\n%%\r\nx = pi/4;\r\ny_correct = 45;\r\nassert(abs(RAD2DEG(x)-y_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":16,"comments_count":0,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2549,"test_suite_updated_at":"2016-10-29T16:53:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-08T10:09:08.000Z","updated_at":"2026-04-02T15:57:17.000Z","published_at":"2016-10-08T10:09:08.000Z","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\",\"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 input in radians, output to degrees\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":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":2094,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-06T15:36:59.000Z","updated_at":"2026-04-01T22:57:48.000Z","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\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}