{"id":442,"date":"2019-06-27T17:52:20","date_gmt":"2019-06-27T17:52:20","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=442"},"modified":"2019-12-20T22:44:22","modified_gmt":"2019-12-20T22:44:22","slug":"reuleaux-wheel","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/reuleaux-wheel\/","title":{"rendered":"Reuleaux Wheel"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"alignright\"><img loading=\"lazy\" decoding=\"async\" width=\"139\" height=\"139\" data-attachment-id=\"1608\" data-permalink=\"https:\/\/math.hmc.edu\/funfacts\/reuleaux-wheel\/20006-2-3-1\/\" data-orig-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/20006.2-3.1.gif\" data-orig-size=\"139,139\" 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=\"20006.2-3.1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/20006.2-3.1.gif\" data-large-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/20006.2-3.1.gif\" src=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/20006.2-3.1.gif\" alt=\"\" class=\"wp-image-1608\"\/><\/figure><\/div>\n\n\n\n<p> A&nbsp;<em>Reuleaux Triangle<\/em>&nbsp;is a plump triangle with rounded edges, formed in the following way: take the three points at the corners of an equilateral triangle, and connect each pair of points by a circular arc centered at the remaining point. <\/p>\n\n\n\n<p>This triangle has some amazing properties. It is&nbsp;<em>constant-width<\/em>, meaning that it will hug parallel lines as it rolls. By rotating the centroid of the Reuleaux triangle appropriately, the figure can be made to trace out a square, perfect except for slightly rounded corners!<\/p>\n\n\n\n<p>This idea has formed the basis of a drill that will carve out squares!<\/p>\n\n\n\n<p>And, what do you think the ratio of its circumference to its width is?<\/p>\n\n\n\n<p>Amazing fact: it is PI!<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Have students think about why this figure is constant width.<\/p>\n\n\n\n<p><strong>The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong><br>There are many other\u00a0convex, constant-width figures, such as the circle and various Reuleaux\u00a0polygons, and they all satisfy the same ratio of\u00a0circumference\u00a0to width!<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong>&nbsp;<br>Su, Francis E., et al. &#8220;Reuleaux Wheel.&#8221;&nbsp;<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts&gt;.<\/p>\n\n\n\n<p><strong>Fun Fact suggested by:  <\/strong> <br>Michael Moody<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A&nbsp;Reuleaux Triangle&nbsp;is a plump triangle with rounded edges, formed in the following way: take the three points at the corners&#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":[20,7,8,4],"class_list":["post-442","page","type-page","status-publish","hentry","tag-analysis","tag-calculus","tag-geometry","tag-medium"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/442","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=442"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/442\/revisions"}],"predecessor-version":[{"id":1609,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/442\/revisions\/1609"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=442"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=442"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}