{"id":1700,"date":"2020-07-25T07:41:53","date_gmt":"2020-07-25T11:41:53","guid":{"rendered":"http:\/\/josmfs.net\/?p=1700"},"modified":"2021-01-05T18:59:27","modified_gmt":"2021-01-05T23:59:27","slug":"the-triangle-of-abul-wafa","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/07\/25\/the-triangle-of-abul-wafa\/","title":{"rendered":"The Triangle of Ab\u016b\u2019l-Waf\u0101\u2019"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1698\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/07\/Triangle-of-Abul-Wafa-Fig2.jpg\" alt=\"\" width=\"252\" height=\"148\" \/>I found an interesting geometric statement in a paper of Glen Van Brummelen cited in the online MAA January 2020 issue of <em><a href=\"https:\/\/www.maa.org\/press\/periodicals\/convergence\/why-history-of-mathematics\">Convergence<\/a><\/em>:<\/p>\n<p>\u201cFor instance, Ab\u016b\u2019l-Waf\u0101\u2019 describes how to embed an equilateral triangle in a square, as follows: extend the base GD by an equal distance to E. Draw a quarter circle with centre G and radius GB; draw a half circle with centre D and radius DE. The two arcs cross at Z. Then draw an arc with centre E and radius EZ downward, to H. If you draw AT = GH and connect B, H, and T, you will have formed the equilateral triangle.\u201d<\/p>\n<p>So the challenge is to prove this statement regarding yet another fascinating appearance of an equilateral triangle.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/07\/Triangle-of-Abul-Wafa-200219.pdf\">Triangle of Ab\u016b\u2019l-Waf\u0101\u2019<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I found an interesting geometric statement in a paper of Glen Van Brummelen cited in the online MAA January 2020 issue of Convergence: \u201cFor instance, Ab\u016b\u2019l-Waf\u0101\u2019 describes how to embed an equilateral triangle in a square, as follows: extend the base GD by an equal distance to E. Draw a quarter circle with centre G [&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":[204,7,13],"class_list":["post-1700","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-abul-wafa","tag-math-history","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1700","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=1700"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1700\/revisions"}],"predecessor-version":[{"id":1951,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1700\/revisions\/1951"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}