{"group":{"group":{"id":96784,"name":"Relationships between areas","lockable":false,"created_at":"2025-11-13T14:02:21.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Correlating areas of different plane figures and finding some relationships.\nThe presented figures were obtained using software MATLAB version R2025b.","is_default":false,"created_by":4993982,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":1,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":7157,"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\u003eCorrelating areas of different plane figures and finding some relationships.\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 presented figures were obtained using software MATLAB version R2025b.\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: 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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 290px 25.5px; transform-origin: 290px 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: 267px 10.5px; text-align: left; transform-origin: 267px 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCorrelating areas of different plane figures and finding some relationships.\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: 267px 10.5px; text-align: left; transform-origin: 267px 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe presented figures were obtained using software MATLAB version R2025b.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2025-12-08T13:43:47.000Z"},"current_player":null},"problems":[{"id":61070,"title":"Square area to triangle area","description":"Given the area, A, of a square with side length, c, if a right angle triangle has the same area A and the hypothenuse length 2c (two times the square side), then find the height, h, of the triangle.\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho","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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 81.875px; transform-origin: 408px 81.875px; 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: 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \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-style: italic; \"\u003ec\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, if a right angle triangle has the same area \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the hypothenuse length \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-style: italic; \"\u003e2c \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(two times the square side), then find the height, \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-style: italic; \"\u003eh\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, of the 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: 0px 0px; transform-origin: 0px 0px; 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: 81.75px; 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 40.875px; transform-origin: 392px 40.875px; 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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eregexp\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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eassignin\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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003estr2num\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: 364px 10.2125px; text-align: left; transform-origin: 364px 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=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A)\r\n  h = A;\r\nend","test_suite":"%%\r\nA = 8;\r\nh_correct = 4;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 9;\r\nh_correct = 3*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 15;\r\nh_correct = sqrt(30);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nh_correct = 4*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 18;\r\nh_correct = 6;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nA = 32;\r\nh_correct = 8;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-09T16:09:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-09T13:39:12.000Z","updated_at":"2026-03-23T20:43:13.000Z","published_at":"2025-11-09T16:09:35.000Z","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 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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\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":61071,"title":"Generalizing square area to triangle area","description":"Cody Problem 61070 asked for the height, h, of a right triangle that had the same area, A, of a square with side length, c, and the hypothenuse length was correlated to the square side by x = 2. \r\nNow, find the height, h, of the right triangle that has the same area, A, of a square with side length, c, and the hypothenuse length is xc, for an arbitrary number x \u003e 2. Here, the height stands for the smallest cathetus.\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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 61.5px; transform-origin: 408px 61.5px; 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: 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 61070\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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for the height, \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-style: italic; \"\u003eh\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, of a right triangle that had the same area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \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-style: italic; \"\u003ec\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 the hypothenuse length was correlated to the square side by \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-style: italic; \"\u003ex = 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: 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: 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNow, find the height, \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-style: italic; \"\u003eh\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, of the right triangle that has the same area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \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-style: italic; \"\u003ec\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 the hypothenuse length is \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-style: italic; \"\u003exc\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, for an arbitrary number \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-style: italic; \"\u003ex \u0026gt; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Here, the height stands for the smallest cathetus.\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 0px; transform-origin: 0px 0px; 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 h = find_height(A,x)\r\n  h = x;\r\nend","test_suite":"%%\r\nA = 9;\r\nx = sqrt(5);\r\nh_correct = 3;\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 10;\r\nx = 3;\r\nh_correct = sqrt(5*(9-sqrt(65)));\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = sqrt(5);\r\nh_correct = 4;\r\nassert(isequal(find_height(A,x),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 16;\r\nx = 3; \r\nh_correct = 4*sqrt((9-sqrt(65))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = 5; \r\nh_correct = 4*sqrt((25 - sqrt(609))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-13T10:09:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2025-11-13T10:09:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-10T14:44:15.000Z","updated_at":"2026-03-23T21:14:52.000Z","published_at":"2025-11-12T17:58:52.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 61070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a right triangle that had the same area, \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, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length was correlated to the square side by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = 2\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\u003eNow, find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the right triangle that has the same area, \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, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exc\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, for an arbitrary number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex \u0026gt; 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, the height stands for the smallest cathetus.\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\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":61074,"title":"Height of a four-pointed star polygon","description":"Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perimeter, and given the total area A_t of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, h, from their bases to the apices, find the vector [l1 l2 h] such that l1\u003cl2.\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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 490.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 245.4px; transform-origin: 408px 245.4px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a rectangle with dimensions \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-style: italic; \"\u003el1xl2\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, where the side lengths are integers and form the smallest possible perimeter, and given the total area \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-style: italic; \"\u003eA_t\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 of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \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-style: italic; \"\u003eh\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, from their bases to the apices, find the vector \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-style: italic; \"\u003e[l1 l2 h]\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 such 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003el1\u0026lt;l2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = star_polygon(A,A_t)\r\n  y = A;\r\nend","test_suite":"%%\r\nA = 10;\r\nA_t = 24;\r\ny_correct = [2 5 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 11;\r\nA_t = 23;\r\ny_correct = [1 11 1];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 72;\r\nA_t = 106;\r\ny_correct = [8 9 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nfiletext = fileread('star_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 156;\r\nA_t = 180;\r\ny_correct = [12 13 0.96];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 168;\r\nA_t = 190;\r\ny_correct = [12 14 11/13];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-14T17:36:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-13T17:02:46.000Z","updated_at":"2026-01-15T09:17:29.000Z","published_at":"2025-11-14T17:36:31.000Z","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 the area \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, of a rectangle with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, from their bases to the apices, find the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1\u0026lt;l2\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\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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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61076,"title":"Covering rectangle area of a four-pointed star polygon","description":"Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from their bases to the apices, find the rectangle, with dimensions y1xy2, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given x=[l1 l2 h], return y=[y1 y2].\r\n\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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 520.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 260.4px; transform-origin: 408px 260.4px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \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-style: italic; \"\u003el1xl2\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 four triangles, with height, \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-style: italic; \"\u003eh,\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 from their bases to the apices, find the rectangle, with dimensions \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-style: italic; \"\u003ey1xy2\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, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex=[l1 l2 h]\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, return \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-style: italic; \"\u003ey=[y1 y2]\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: 418.8px; 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 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; 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: 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 0px; transform-origin: 0px 0px; 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 y = covering(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [2 7 4];\r\ny_correct = [5 10];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 2 1];\r\ny_correct = [2.5 -2.5] + 1.5*sqrt(13);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nx = [5 2 1];\r\ny_correct = [3 -3]/2 + sqrt(77)/2;\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('covering.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = [7 9 5];\r\ny_correct = [11 13];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 9 1];\r\ny_correct = [-1 1] + 4*sqrt(5);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-16T14:03:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-15T16:57:30.000Z","updated_at":"2026-03-27T12:50:09.000Z","published_at":"2025-11-16T14:03:25.000Z","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 the four-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1xy2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey=[y1 y2]\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\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 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61081,"title":"Slicing the area of a regular polygon","description":"Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n\u003e3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.\r\nHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\r\ninput: (A, n)\r\noutput: y = [L h A_r]\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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 575.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 287.9px; transform-origin: 408px 287.9px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a regular polygon 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: 0px 0px; transform-origin: 0px 0px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides, each of length \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-style: italic; \"\u003es\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, consider its decomposition in congruent isosceles triangles of base \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-style: italic; \"\u003es\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 heigth \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-style: italic; \"\u003eh\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. Find the rectangle, with dimensions \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-style: italic; \"\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×\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-style: italic; \"\u003eh\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, which covers all \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangles in their adjacent positions (\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-style: italic; \"\u003en\u0026gt;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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cf. figure below). Complete the problem by determining the area, \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-style: italic; \"\u003eA_r\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, of the rectangle.\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003e(A, n)\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003ey = [L h A_r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 413.8px; 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 206.9px; text-align: left; transform-origin: 385px 206.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"501\" height=\"408\" style=\"vertical-align: baseline;width: 501px;height: 408px\" src=\"data:image/png;base64,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\" alt=\"Slicing square (n=4)\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = slicing(A,n)\r\n  y = [L h A_r];\r\nend","test_suite":"%%\r\nA = 16;\r\nn = 4;\r\ny_correct = [10 2 20];\r\nassert(isequal(slicing(A,n),y_correct))\r\n\r\n%%\r\nA = 20;\r\nn = 5; \r\ny_correct = [10.22849568767431 2.34638608968871 24];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 20;\r\nn = 6; \r\ny_correct = [7*sqrt(10*3^(-3/2)) sqrt(10*3^(-1/2)) 70/3];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nA = 32;\r\nn = 8; \r\ny_correct = [18*sqrt(sqrt(2)-1) 2/sqrt(sqrt(2)-1) 36];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-19T14:59:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-18T11:18:12.000Z","updated_at":"2026-03-20T13:59:51.000Z","published_at":"2025-11-19T14:59:52.000Z","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 the area, \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, of a regular polygon with \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 sides, each of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and heigth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which covers all \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 triangles in their adjacent positions (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;3,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cf. figure below). Complete the problem by determining the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle.\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\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, 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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\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\u003ey = [L h A_r]\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=\\\"408\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"501\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61082,"title":"Slicing the area of a circle","description":"Given the area, A, of a square, consider a circle having the area, πA, and the radius, r.\r\nFor a given slicing number n\u003e1, find the (n+1)×2 matrix, M = [A1/π a1; A2/π a2; ...; An/π an; A_r L], where\r\nin the first row (i=1), A1 stands for the area of one slice (like a pizza slice), and a1 stands for the logical 1 if A1 is smaller than or reaches the square's area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of two slices and a2 has the same previous false-true meaning relative to the areas A2 and A;\r\nand so on, until last slice of the circle;\r\nin the last row (i=n+1), A_r is the area of the rectangle, with dimensions L×r, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\r\nHint: Compare with Problem 61081.\r\ninput: (A,n)\r\noutput:  M = [A1/π a1; A2/π a2; ...; An/π an; A_r L]","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: 325.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 162.75px; transform-origin: 408px 162.75px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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 the area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square, consider a circle having the area, \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-style: italic; \"\u003eπA,\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 the 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-style: italic; \"\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: 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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=\"\"\u003eFor a given slicing number \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-style: italic; \"\u003en\u0026gt;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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \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-style: italic; \"\u003e(n+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: 0px 0px; transform-origin: 0px 0px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\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 matrix, \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-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\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, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 163.5px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 81.75px; transform-origin: 391px 81.75px; margin-top: 10px; margin-bottom: 20px; \"\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: 363px 20.4375px; text-align: left; transform-origin: 363px 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=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\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=\"\"\u003e, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the area of one slice (like a pizza slice), and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\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=\"\"\u003e if \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e is smaller than or reaches the square's area \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\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=\"\"\u003e or \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\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=\"\"\u003e if \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\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=\"\"\u003e;\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: 363px 20.4375px; text-align: left; transform-origin: 363px 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=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\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=\"\"\u003e, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the area of two slices and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\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=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\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=\"\"\u003e and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\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=\"\"\u003e;\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: 363px 10.2125px; text-align: left; transform-origin: 363px 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=\"\"\u003eand so on, until last slice of the circle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; 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: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; 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=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=n+1),\u003c/span\u003e\u003c/span\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=\"\"\u003e \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\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=\"\"\u003e is the area of the rectangle, with dimensions \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\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=\"\"\u003e×\u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\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=\"\"\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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=\"\"\u003eHint: Compare with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\"\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=\"\"\u003eProblem 61081\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: 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: 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003e(A,n)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_circle(A,n)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 8;\r\nn = 4;\r\ny_correct = [2 1; 4 0; 6 0; 8 0; 8*sqrt(2) 4];\r\nY = slicing_circle(A,n);\r\ntolerance = 1e-13;\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 ...\r\n    abs(Y(end)-y_correct(end)) \u003c tolerance \u0026 all(Y(1:end,2) == y_correct(1:end,2)))\r\n\r\n%%\r\nA = 36;\r\nn = 6;\r\ny_correct = [6 1; 12 0; 18 0; 24 0; 30 0; 36 0; 36 6];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n\r\n%%\r\nA = 36;\r\nn = 12;\r\ny_correct = [3 1; 6 1; 9 1; 12 0; 15 0; 18 0; 21 0; 24 0; 27 0; 30 0; 33 0; 36 0; ...\r\n    37.92731310242232  6.32121885040372];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing_circle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 70;\r\nn = 7;\r\ny_correct = [10 1; 20 1; 30 0; 40 0; 50 0; 60 0; 70 0; ...\r\n    94.4539467929851 11.28940594715244];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nA = 70;\r\nn = 10;\r\ny_correct = [7 1; 14 1; 21 1; 28 0; 35 0; 42 0; 49 0; 56 0; 63 0; 70 0; ...\r\n    88.7511366850995 10.6077897676978];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026  all(Y(1:n,2) == y_correct(1:n,2))  \u0026  ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))","published":true,"deleted":false,"likes_count":0,"comments_count":10,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-27T14:44:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2025-11-27T14:44:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-20T14:17:04.000Z","updated_at":"2025-12-17T10:09:27.000Z","published_at":"2025-11-21T15:27:17.000Z","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 the area, \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, of a square, consider a circle having the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eπA,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\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:t\u003eFor a given slicing number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(n+1)\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\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\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\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one slice (like a pizza slice), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the square's area \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 or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \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;\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\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\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\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\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\u003eA\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=\\\"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\u003eand so on, until last slice of the circle;\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\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=n+1),\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_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\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\u003eHint: Compare with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61081\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A,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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \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\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\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":61086,"title":"Covering a four-pointed star polygon by rectangles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).\r\nGiven (A, L), return the 2x2 matrix M, where \r\nthe first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);\r\nthe second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).\r\ninput: (A, L)\r\noutput: M = [y1 y2; z1 z2]\r\n","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: 635.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 317.837px; transform-origin: 408px 317.837px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; 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 the area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \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-style: italic; \"\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×\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-style: italic; \"\u003e2L\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 four triangles, with height \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-style: italic; \"\u003eh\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 from their bases to the vertices, find the rectangles that have the same area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and cover the distance between opposite vertices (cf. figure below).\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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 \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-style: italic; \"\u003e(A, L)\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, return the \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-style: italic; \"\u003e2\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=\"\"\u003ex\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-style: italic; \"\u003e2\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 matrix \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-style: italic; \"\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=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 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=\"\"\u003ethe first row returns the dimensions, y\u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\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=\"\"\u003e×\u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ey2\u003c/span\u003e\u003c/span\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=\"\"\u003e, of the rectangle that covers the minimum distance (cf. left figure);\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: 363px 10.2125px; text-align: left; transform-origin: 363px 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=\"\"\u003ethe second row returns the dimensions, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ez1\u003c/span\u003e\u003c/span\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=\"\"\u003e×z\u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\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=\"\"\u003e, of the rectangle that covers the maximum distance (cf. right figure).\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003e(A, L)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003eM = [y1 y2; z1 z2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 411.8px; 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: 384px 205.9px; text-align: left; transform-origin: 384px 205.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"406\" style=\"vertical-align: baseline;width: 508px;height: 406px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_polygon(A,L)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nL = 3;\r\nM_correct = [5 5.4; 3.375 8];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 36;\r\nL = 3;\r\nM_correct = [7 36/7; 3.6 10];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('covering_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 48;\r\nL = 4;\r\nM_correct = [20/3 36/5; 4.5 32/3];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 56;\r\nL = 4;\r\nM_correct = [8 7; 14/3 12];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-28T15:21:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-27T15:06:59.000Z","updated_at":"2026-03-21T13:41:00.000Z","published_at":"2025-11-28T15:21:25.000Z","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 the area, \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, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, find the rectangles that have the same area, \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, and cover the distance between opposite vertices (cf. 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:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle that covers the maximum distance (cf. right 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:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61088,"title":"Covering a four-pointed star polygon by circles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\r\nGiven (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where\r\nin the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 \u003e A holds true, then a2 = 0.\r\ninput: (A, h)\r\noutput: M = [A1/π a1; A2/π 0]\r\n","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: 748.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 374.487px; transform-origin: 408px 374.494px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; 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 the area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \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-style: italic; \"\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×\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-style: italic; \"\u003e2L\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 four triangles, with height \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-style: italic; \"\u003eh\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 from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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 \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-style: italic; \"\u003e(A,h)\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, return the \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-style: italic; \"\u003e2\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=\"\"\u003ex\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-style: italic; \"\u003e2\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 matrix \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-style: italic; \"\u003eM = [A1/π a1; A2/π a2]\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, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\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: 363px 20.4375px; text-align: left; transform-origin: 363px 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=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\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=\"\"\u003e, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\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=\"\"\u003e if \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e is smaller than or reaches the area \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\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=\"\"\u003e or \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\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=\"\"\u003e if \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\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=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; 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: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; 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=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\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=\"\"\u003e, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\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=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\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=\"\"\u003e and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\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=\"\"\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea2 = 0\u003c/span\u003e\u003c/span\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=\"\"\u003e.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003e(A, h)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003eM = [A1/π a1; A2/π 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; 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: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" alt=\"Covering by circles\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_by_circles(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [6.25 1; 16 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [12.25 0; 25 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 56;\r\nh = 2;\r\nM_correct = [16 1; 36 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_circles.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [13.69 1; 38.44 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [26.01 1; 57.76 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-30T13:14:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-29T14:26:03.000Z","updated_at":"2026-03-22T14:02:11.000Z","published_at":"2025-11-30T13:14:56.000Z","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 the area, \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, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. 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:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\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\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the area \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 or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \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;\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\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\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\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\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\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2 = 0\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, h)\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:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61090,"title":"Covering a 4-pointed star polygon by a circle sector","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\r\nGiven (A,h), find\r\nthe width, L, of the rectangle;\r\nthe angle, α [in Radians], of the sector of the circle such that its area is equal to A;\r\nthe minimum slicing number n, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\r\ninput: (A, h)\r\noutput: y = [L alpha n]\r\n","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: 751.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 375.775px; transform-origin: 408px 375.775px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; 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 the area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \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-style: italic; \"\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×\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-style: italic; \"\u003e2L\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 four triangles, with height \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-style: italic; \"\u003eh\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 from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure below).\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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 \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-style: italic; \"\u003e(A,h)\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, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 40.875px; transform-origin: 391px 40.875px; 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: 363px 10.2125px; text-align: left; transform-origin: 363px 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=\"\"\u003ethe width, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eL,\u003c/span\u003e\u003c/span\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=\"\"\u003e of the rectangle;\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: 363px 10.2125px; text-align: left; transform-origin: 363px 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=\"\"\u003ethe angle, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eα\u003c/span\u003e\u003c/span\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=\"\"\u003e [in Radians], of the sector of the circle such that its area is equal to \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\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=\"\"\u003e;\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: 363px 20.4375px; text-align: left; transform-origin: 363px 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=\"\"\u003ethe minimum slicing number \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\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=\"\"\u003e, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003e(A, h)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003ey = [L alpha n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 486.8px; 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: 384px 243.4px; text-align: left; transform-origin: 384px 243.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"481\" style=\"vertical-align: baseline;width: 601px;height: 481px\" 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\" alt=\"Covering by sector\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering_by_sector(A,h)\r\n  y = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\ny_correct = [3 3.375 2];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\ny_correct = [3 2.88 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nA = 45;\r\nh = 3;\r\ny_correct = [3 2.5 3];\r\nassert(isequal(covering_by_sector(A,h),y_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_sector.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 56;\r\nh = 2; \r\ny_correct = [4 28/9 3];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n\r\n%%\r\nA = 50;\r\nh = 5; \r\ny_correct = [2.5 16/9 4];\r\nassert(all(isapprox(covering_by_sector(A,h),y_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-03T10:39:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-30T14:56:09.000Z","updated_at":"2026-03-23T10:36:12.000Z","published_at":"2025-12-03T10:39:21.000Z","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 the area, \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, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circle that covers the greater of the two distances between opposite vertices (cf. figure 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61091,"title":"Slicing a 4-pointed star polygon","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the area, A_r, of the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \r\nGiven (A,h), find the 9×2 matrix, M = [A1 a1; A2 a2; ...; A8 a8; A_r/π n], where\r\nin the first row (i=1), A1 stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and a1 stands for the logical 1 if A1 does not exceed the circle's area, A_r, or a1 stands for the logical 0 otherwise;\r\nin the second row (i=2), A2 stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and a2 has the same previous false-true meaning relative to the areas A2 and A_r;\r\nand so on, until last slice of the 4-pointed star polygon;\r\nin the last row (i=9), A_r is the area of the circle, and n stands for the maximum number of slices that their cumulative area does not exceed the circle area.\r\nHint: The slices of the 4-pointed star polygon are not congruent among each other.\r\ninput: (A, h)\r\noutput: M = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\r\n","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: 840.862px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 420.425px; transform-origin: 408px 420.431px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; 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 the area, \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-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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \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-style: italic; \"\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×\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-style: italic; \"\u003e2L\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 four triangles, with height \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-style: italic; \"\u003eh\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 from their bases to the vertices, consider the area, \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-style: italic; \"\u003eA_r, \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=\"\"\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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 \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-style: italic; \"\u003e(A,h)\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, find the \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-style: italic; \"\u003e9\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003e2\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 matrix, \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-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\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, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 143.062px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 71.525px; transform-origin: 391px 71.5312px; margin-top: 10px; margin-bottom: 20px; \"\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: 363px 20.4375px; text-align: left; transform-origin: 363px 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=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\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=\"\"\u003e, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\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=\"\"\u003e if \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\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=\"\"\u003e does not exceed the circle's area, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA_r,\u003c/span\u003e\u003c/span\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=\"\"\u003e or \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\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=\"\"\u003e otherwise;\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: 363px 20.4375px; text-align: left; transform-origin: 363px 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=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\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=\"\"\u003e, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\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=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\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=\"\"\u003e and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\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=\"\"\u003e;\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: 363px 10.2125px; text-align: left; transform-origin: 363px 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=\"\"\u003eand so on, until last slice of the 4-pointed star polygon;\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: 363px 20.4375px; text-align: left; transform-origin: 363px 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=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003e(i=9)\u003c/span\u003e\u003c/span\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=\"\"\u003e, \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\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=\"\"\u003e is the area of the circle, and \u003c/span\u003e\u003c/span\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=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\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=\"\"\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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=\"\"\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003e(A, h)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; 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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; 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: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_star(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [3 1; 6.75 1; 10.5 1; 13.5 1; 16.5 1; 20.25 0; 24 0; 27 0; 6.25 5];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [3.75 1; 9 1; 14.25 1; 18 1; 21.75 1; 27 1; 32.25 1; 36 1; 12.25 8];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('slicing_star.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [7.75 1; 17 1; 26.25 1; 34 1; 41.75 1; 51 0; 60.25 0; 68 0; 13.69 5];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [9.5 1; 22.25 1; 35 1; 44.5 1; 54 1; 66.75 1; 79.5 1; 89 0; 26.01 7];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-08T13:42:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-03T13:58:16.000Z","updated_at":"2025-12-19T15:03:36.000Z","published_at":"2025-12-08T13:42:41.000Z","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 the area, \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, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\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\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right 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:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\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\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\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\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\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\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not exceed the circle's area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e otherwise;\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\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\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\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\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\u003eA_r\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=\\\"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\u003eand so on, until last slice of the 4-pointed star polygon;\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\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=9)\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_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the circle, and \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 stands for the maximum number of slices that their cumulative area does not exceed the circle area.\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\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\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(A, h)\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\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\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/r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