{"id":1162,"date":"2019-07-13T10:12:50","date_gmt":"2019-07-13T14:12:50","guid":{"rendered":"http:\/\/josmfs.net\/?p=1162"},"modified":"2019-07-14T09:55:35","modified_gmt":"2019-07-14T13:55:35","slug":"magic-pythagorean-circle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/07\/13\/magic-pythagorean-circle\/","title":{"rendered":"Magic Pythagorean Circle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1168\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/07\/Magic-Pythagorean-Circle-Fig2.jpg\" alt=\"\" width=\"204\" height=\"154\" \/>This statement showed up recently at <a href=\"https:\/\/www.futilitycloset.com\/2019\/07\/09\/neat-4\/\">Futility Closet<\/a> and I found it to be another one of those magical results that seemed so surprising. I don\u2019t recall ever seeing this before.<\/p>\n<p>\u201cThe radius of a circle inscribed in a 3-4-5 triangle is 1.<br \/>\n(In fact, <strong>the inradius of any Pythagorean triangle is an integer<\/strong>.)\u201d<\/p>\n<p>(A Pythagorean triangle is a right triangle whose sides form a Pythagorean triple.) Futility Closet left these remarkable statements unproven, so naturally I felt I had to provide a proof.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/07\/Magic-Pythagorean-Circle-190713a.pdf\">Magic Pythagorean Circle<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This statement showed up recently at Futility Closet and I found it to be another one of those magical results that seemed so surprising. I don\u2019t recall ever seeing this before. \u201cThe radius of a circle inscribed in a 3-4-5 triangle is 1. (In fact, the inradius of any Pythagorean triangle is an integer.)\u201d (A [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[16,30],"class_list":["post-1162","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-futility-closet","tag-pythagorean-theorem"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1162","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=1162"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1162\/revisions"}],"predecessor-version":[{"id":1170,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1162\/revisions\/1170"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}