{"id":190,"date":"2019-06-26T22:57:20","date_gmt":"2019-06-26T22:57:20","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=190"},"modified":"2020-01-03T22:25:24","modified_gmt":"2020-01-03T22:25:24","slug":"suspended-rope-trick","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/suspended-rope-trick\/","title":{"rendered":"Suspended Rope Trick"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"alignright\"><img loading=\"lazy\" decoding=\"async\" width=\"223\" height=\"56\" data-attachment-id=\"1671\" data-permalink=\"https:\/\/math.hmc.edu\/funfacts\/suspended-rope-trick\/10001-3-1-2\/\" data-orig-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2020\/01\/10001.3.1.gif\" data-orig-size=\"223,56\" 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=\"10001.3.1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2020\/01\/10001.3.1.gif\" data-large-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2020\/01\/10001.3.1.gif\" src=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2020\/01\/10001.3.1.gif\" alt=\"\" class=\"wp-image-1671\"\/><\/figure><\/div>\n\n\n\n<p>What is the shape of a suspended rope? Is there some function that describes it?<\/p>\n\n\n\n<p>Answer: it&#8217;s the cosh curve!<\/p>\n\n\n\n<p><strong>Presentation\u00a0Suggestions:<\/strong><br>This may be seen quite dramatically by putting up a transparency of the catenary<\/p>\n\n\n\n<p style=\"text-align:center\">y = cosh x<\/p>\n\n\n\n<p>and suspending a rope in front of the transparency projection so that the rope shadow can be compared!<\/p>\n\n\n\n<p>Now, someone may object and say that the curve of x<sup>2<\/sup>&nbsp;will also give a good approximation. If they do this, you can talk about how the Taylor series of cosh begins with a quadratic 1 + x<sup>2<\/sup>\/2, so it is not surprising!<\/p>\n\n\n\n<p><strong>The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong><br>Calculus\u00a0and modeling are useful here: by breaking the rope into lots of little chunks, and modeling the forces on each chunk, one can obtain a\u00a0differential equation\u00a0whose solution is the cosh curve.<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong>&nbsp;<br>Su, Francis E., et al. &#8220;Suspended Rope Trick.&#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>What is the shape of a suspended rope? Is there some function that describes it? Answer: it&#8217;s the cosh curve!&#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":[20,7,40,3,173],"class_list":["post-190","page","type-page","status-publish","hentry","tag-analysis","tag-calculus","tag-demonstration","tag-easy","tag-taylor-series"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/190","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=190"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/190\/revisions"}],"predecessor-version":[{"id":1672,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/190\/revisions\/1672"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=190"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}