{"id":2468,"date":"2021-11-20T08:06:30","date_gmt":"2021-11-20T13:06:30","guid":{"rendered":"https:\/\/josmfs.net\/?p=2468"},"modified":"2021-11-20T08:06:30","modified_gmt":"2021-11-20T13:06:30","slug":"tethered-triangle-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/11\/20\/tethered-triangle-puzzle\/","title":{"rendered":"Tethered Triangle Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2466\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Tethered-Triangle-Fig2.jpg\" alt=\"\" width=\"200\" height=\"161\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Tethered-Triangle-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Tethered-Triangle-Fig2-300x242.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is another problem from MEI\u2019s MathsMonday.<\/p>\n<p>\u201cTwo equilateral triangles share a common vertex. Show that the lengths marked <em>a<\/em> and <em>b<\/em> are equal for any such arrangement.\u201d<\/p>\n<p>This seems quite amazing at first.\u00a0 One can picture the small triangle swinging back and forth with red bungee chords tethering its bottom vertices to the bottom vertices of the large triangle.\u00a0 It would seem remarkable that the lengths of the chords would remain equal to each other throughout.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Tethered-Triangle-211016.pdf\">Tethered Triangle Puzzle<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another problem from MEI\u2019s MathsMonday. \u201cTwo equilateral triangles share a common vertex. Show that the lengths marked a and b are equal for any such arrangement.\u201d This seems quite amazing at first.\u00a0 One can picture the small triangle swinging back and forth with red bungee chords tethering its bottom vertices to the bottom [&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-2468","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\/2468","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=2468"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2468\/revisions"}],"predecessor-version":[{"id":2469,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2468\/revisions\/2469"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2468"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2468"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2468"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}