{"id":309,"date":"2019-06-26T23:32:23","date_gmt":"2019-06-26T23:32:23","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=309"},"modified":"2019-12-09T21:39:00","modified_gmt":"2019-12-09T21:39:00","slug":"napoleons-theorem","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/napoleons-theorem\/","title":{"rendered":"Napoleon&#8217;s Theorem"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"alignright\"><img loading=\"lazy\" decoding=\"async\" width=\"148\" height=\"225\" data-attachment-id=\"1541\" data-permalink=\"https:\/\/math.hmc.edu\/funfacts\/napoleons-theorem\/10009-2-1\/\" data-orig-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10009.2.1.gif\" data-orig-size=\"148,225\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"10009.2.1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10009.2.1.gif\" data-large-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10009.2.1.gif\" src=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10009.2.1.gif\" alt=\"\" class=\"wp-image-1541\"\/><\/figure><\/div>\n\n\n\n<p>Take any generic triangle, and construct equilateral triangles on each side whose side lengths are the same as the length of each side of the original triangle.<\/p>\n\n\n\n<p>Surprise: the centers of the equilateral triangles form an\u00a0equilateral triangle!<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Show the truth of the statement using some extreme cases for the initial triangle (a particularly instructive example is a triangle with one sidelength very close to zero).<\/p>\n\n\n\n<p><strong>The&nbsp;Math&nbsp;Behind&nbsp;the&nbsp;Fact:<\/strong><br>This theorem is credited to Napoleon, who was fond of mathematics, though many doubt that he knew enough math to discover it!<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong><br>Su, Francis E., et al. &#8220;Napoleon&#8217;s Theorem.&#8221;&nbsp;<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts&gt;.\n\n<\/p>\n\n\n\n<p><strong>Fun Fact suggested by:   <\/strong><br>Michael Moody <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Take any generic triangle, and construct equilateral triangles on each side whose side lengths are the same as the length&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,8,163],"class_list":["post-309","page","type-page","status-publish","hentry","tag-easy","tag-geometry","tag-triangles"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/309","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=309"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/309\/revisions"}],"predecessor-version":[{"id":1542,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/309\/revisions\/1542"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=309"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}