{"id":2157,"date":"2021-06-05T09:59:37","date_gmt":"2021-06-05T13:59:37","guid":{"rendered":"https:\/\/josmfs.net\/?p=2157"},"modified":"2021-06-05T09:59:37","modified_gmt":"2021-06-05T13:59:37","slug":"area-vs-perimeter-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/06\/05\/area-vs-perimeter-puzzle\/","title":{"rendered":"Area vs. Perimeter Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2155\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-fig2.jpg\" alt=\"\" width=\"252\" height=\"87\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-fig2.jpg 501w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-fig2-300x104.jpg 300w\" sizes=\"auto, (max-width: 252px) 100vw, 252px\" \/>This surprising, but simple, puzzle is from the 12 April MathsMonday <a href=\"https:\/\/twitter.com\/Beamathsteacher\/status\/1381577925657571330\">offering<\/a> by MEI, an independent curriculum development body for mathematics education in the UK.<\/p>\n<p>\u201cIn the diagram various regular polygons, P, have been drawn whose sides are tangents to a circle, C.\u00a0 Show that for any regular polygon drawn in this way:\u201d<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2156 aligncenter\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-Ratio.jpg\" alt=\"\" width=\"319\" height=\"54\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-Ratio.jpg 770w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-Ratio-300x51.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-Ratio-768x131.jpg 768w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimiter-Ratio-624x106.jpg 624w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>(Given that the polygons approximate the circle in the limit, it would not be surprising that this relationship would hold\u2014<em>in the limit<\/em>.\u00a0 It <em>is<\/em> surprising that it should be true for every regular polygon that circumscribes the circle.)<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Area-vs-Perimeter-Puzzle-210604.pdf\">Area vs. Perimeter Puzzle<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This surprising, but simple, puzzle is from the 12 April MathsMonday offering by MEI, an independent curriculum development body for mathematics education in the UK. \u201cIn the diagram various regular polygons, P, have been drawn whose sides are tangents to a circle, C.\u00a0 Show that for any regular polygon drawn in this way:\u201d (Given that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[213,13],"class_list":["post-2157","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-mathsmonday","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2157","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2157"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2157\/revisions"}],"predecessor-version":[{"id":2158,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2157\/revisions\/2158"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}