{"id":67,"date":"2010-07-13T16:01:41","date_gmt":"2010-07-13T16:01:41","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=67"},"modified":"2025-01-27T09:41:32","modified_gmt":"2025-01-27T14:41:32","slug":"fun-with-geometry","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/difficulty\/hard\/fun-with-geometry\/","title":{"rendered":"Fun with Geometry"},"content":{"rendered":"<p>Consider a pentagram (see picture below). There are five disjoint triangles initially.  Just count the five &#8216;caps&#8217; above the pentagon, do not count the larger triangles formed by using three of the five vertices, for those &#8216;triangles&#8217; have lines going through them. By adding just two lines, you can go from five to 10 disjoint triangles.  How?<\/p>\n<p>Submitted by Bruce Lin, from friends at MIT, who got it from Andrew Russell, a graduate student in EE at MIT, who either made it up or got it from&#8230;?<\/p>\n<p><a href=\"https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/triangle.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-68\" title=\"triangle\" src=\"https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/triangle-300x249.jpg\" alt=\"triangle\" width=\"300\" height=\"249\" srcset=\"https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/triangle-300x249.jpg 300w, https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/triangle-361x300.jpg 361w, https:\/\/sites.williams.edu\/mathriddles\/files\/2010\/07\/triangle.jpg 589w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider a pentagram (see picture below). There are five disjoint triangles initially. Just count the five &#8216;caps&#8217; above the pentagon, do not count the larger triangles formed by using three of the five vertices, for those &#8216;triangles&#8217; have lines going through them. By adding just two lines, you can go from five to 10 disjoint&hellip;<\/p>\n","protected":false},"author":2861,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[15,6],"tags":[],"class_list":["post-67","post","type-post","status-publish","format-standard","hentry","category-geometry","category-hard"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/users\/2861"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/comments?post=67"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/67\/revisions"}],"predecessor-version":[{"id":1183,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/67\/revisions\/1183"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=67"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=67"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}