{"id":532,"date":"2019-01-20T16:14:46","date_gmt":"2019-01-20T21:14:46","guid":{"rendered":"http:\/\/josmfs.net\/?p=532"},"modified":"2019-03-27T23:31:19","modified_gmt":"2019-03-28T03:31:19","slug":"containing-an-arc","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/01\/20\/containing-an-arc\/","title":{"rendered":"Containing an Arc"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-528\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Containing-an-Arc-Fig.jpg\" alt=\"\" width=\"200\" height=\"67\" \/>This problem from <a href=\"https:\/\/www.futilitycloset.com\/\">Futility Closet<\/a> proved quite challenging.<\/p>\n<p>\u201cUniversity of Illinois mathematician John Wetzel called this one of his favorite problems in geometry. Call a plane arc special if it has length 1 and lies on one side of the line through its end points. Prove that any special arc can be contained in an isosceles right triangle of hypotenuse 1.\u201d<\/p>\n<p>My attempts were futile (maybe that is where the title of the website comes from). Maybe this qualifies for another Coffin Problem. But I did have one little comment about the Futility Closet solution. See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Containing-an-Arc-190120.pdf\">Containing an Arc<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This problem from Futility Closet proved quite challenging. \u201cUniversity of Illinois mathematician John Wetzel called this one of his favorite problems in geometry. Call a plane arc special if it has length 1 and lies on one side of the line through its end points. Prove that any special arc can be contained in an [&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":[71,16,13,73],"class_list":["post-532","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-coffin-problem","tag-futility-closet","tag-plane-geometry","tag-symmetries"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/532","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=532"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/532\/revisions"}],"predecessor-version":[{"id":815,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/532\/revisions\/815"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=532"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=532"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=532"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}