{"id":1802,"date":"2020-10-10T08:35:34","date_gmt":"2020-10-10T12:35:34","guid":{"rendered":"http:\/\/josmfs.net\/?p=1802"},"modified":"2021-01-05T18:49:42","modified_gmt":"2021-01-05T23:49:42","slug":"circle-halving-zigzag-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/10\/10\/circle-halving-zigzag-problem\/","title":{"rendered":"Circle-Halving Zigzag Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1800\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/10\/Circle-Halving-Zigzag-Fig.jpg\" alt=\"\" width=\"200\" height=\"222\" \/>This is another delightful Brainteaser from the <em>Quantum<\/em> math magazine.<\/p>\n<p>\u201cAll the vertices of a polygonal line ABCDE lie on a circumference (see the figure), and the angles at the vertices B, C, and D are each 45\u00b0.<\/p>\n<p>Prove that the area of the blue part of the circle is equal to the area of the yellow part. (V. Proizvolov)\u201d<\/p>\n<p>I especially liked this problem since I was able to find a solution different from the one given by <em>Quantum<\/em>.\u00a0 Who knows how many other variations there might be.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/10\/Circle-Halving-Zigzag-200726.pdf\">Circle-Halving Zigzag Problem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another delightful Brainteaser from the Quantum math magazine. \u201cAll the vertices of a polygonal line ABCDE lie on a circumference (see the figure), and the angles at the vertices B, C, and D are each 45\u00b0. Prove that the area of the blue part of the circle is equal to the area of [&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":[13,194],"class_list":["post-1802","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-quantum-magazine"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1802","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=1802"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1802\/revisions"}],"predecessor-version":[{"id":1935,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1802\/revisions\/1935"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1802"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1802"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}