{"id":2279,"date":"2021-07-03T09:42:01","date_gmt":"2021-07-03T13:42:01","guid":{"rendered":"https:\/\/josmfs.net\/?p=2279"},"modified":"2021-07-03T09:42:01","modified_gmt":"2021-07-03T13:42:01","slug":"bottemas-theorem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/07\/03\/bottemas-theorem\/","title":{"rendered":"Bottema\u2019s Theorem"},"content":{"rendered":"

\"\"<\/p>\n

This seemingly magical result from Futility Closet<\/a> defies proof at first.\u00a0 Go to the Wolfram demo<\/a> by Jay Warendorff and then \u2026<\/p>\n

\u201cGrab point B above and drag it to a new location. Surprisingly, M, the midpoint of RS, doesn\u2019t move.<\/p>\n

This works for any triangle \u2014 draw squares on two of its sides, note their common vertex, and draw a line that connects the vertices of the respective squares that lie opposite that point. Now changing the location of the common vertex does not change the location of the midpoint of the line.<\/p>\n

It was discovered by Dutch mathematician Oene Bottema.\u201d<\/p>\n

As we shall see, Bottema\u2019s Theorem has shown up in other guises as well.<\/p>\n

See Bottema\u2019s Theorem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

This seemingly magical result from Futility Closet defies proof at first.\u00a0 Go to the Wolfram demo by Jay Warendorff and then \u2026 \u201cGrab point B above and drag it to a new location. Surprisingly, M, the midpoint of RS, doesn\u2019t move. This works for any triangle \u2014 draw squares on two of its sides, note […]<\/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":[51,16,155,13,31],"class_list":["post-2279","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-complex-numbers","tag-futility-closet","tag-george-gamow","tag-plane-geometry","tag-vectors"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2279","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=2279"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2279\/revisions"}],"predecessor-version":[{"id":2280,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2279\/revisions\/2280"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}