{"id":389,"date":"2019-01-04T14:44:40","date_gmt":"2019-01-04T19:44:40","guid":{"rendered":"http:\/\/josmfs.net\/wordpress\/?p=389"},"modified":"2019-01-04T15:24:04","modified_gmt":"2019-01-04T20:24:04","slug":"polygon-altitude-problems-i","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/01\/04\/polygon-altitude-problems-i\/","title":{"rendered":"Polygon Altitude Problems I"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-381\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Polygon-Altitude-Prob-I-Triangle.jpg\" alt=\"\" width=\"200\" height=\"174\" \/>I found this collection of related problems by <a href=\"https:\/\/twitter.com\/jamestanton\">James Tanton<\/a> on Twitter. Even though all these problems do not involve perpendiculars, they have a common solution approach \u2013 a sort of theme and variations idea. In a later tweet Tanton refers to a Viviani Theorem associated with these types of problems. I did not recall that theorem explicitly or by name. I also have not looked it up yet, in order to solve these problems on my own. I am guessing there is a more classical Euclidean geometry proof, but I like my vector approach for its clarity. I also throw in a bit a calculus at the end for fun. See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Polygon-Altitude-Problems-I-180827.pdf\">Polygon Altitude Problems I<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I found this collection of related problems by James Tanton on Twitter. Even though all these problems do not involve perpendiculars, they have a common solution approach \u2013 a sort of theme and variations idea. In a later tweet Tanton refers to a Viviani Theorem associated with these types of problems. I did not recall [&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":[32,43,13,31,44],"class_list":["post-389","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-calculus","tag-james-tanton","tag-plane-geometry","tag-vectors","tag-viviani-theorem"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/389","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=389"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/389\/revisions"}],"predecessor-version":[{"id":397,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/389\/revisions\/397"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}