{"id":263,"date":"2019-06-26T23:15:53","date_gmt":"2019-06-26T23:15:53","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=263"},"modified":"2019-11-22T20:19:45","modified_gmt":"2019-11-22T20:19:45","slug":"holey-beads","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/holey-beads\/","title":{"rendered":"Holey Beads"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"alignright\"><img loading=\"lazy\" decoding=\"async\" width=\"252\" height=\"50\" data-attachment-id=\"1469\" data-permalink=\"https:\/\/math.hmc.edu\/funfacts\/holey-beads\/10004-3-1\/\" data-orig-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/11\/10004.3.1.gif\" data-orig-size=\"252,50\" 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=\"10004.3.1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/11\/10004.3.1.gif\" src=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/11\/10004.3.1.gif\" alt=\"\" class=\"wp-image-1469\"\/><\/figure><\/div>\n\n\n\n<p>Take a bead 5 inches high, and bore a hole through it from north pole to south pole in such a way that the part which remains is 4 inches high (measured lengthwise through the hole).<\/p>\n\n\n\n<p>Now take a bead 5 feet high, and bore a hole through it in the same fashion, so that the part which remains is also 4 inches high (you&#8217;ll have to bore a very large hole).<\/p>\n\n\n\n<p>Surprisingly, the volumes of the two &#8220;holey&#8221; beads are now exactly the same! (In fact, the same volume as a 4-inch bead with no hole!) Actually, it doesn&#8217;t matter how big the bead is that you start with&#8230; you could have started with the Moon, and it would still be true.<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Draw suggestive pictures!<\/p>\n\n\n\n<p><strong>The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong><br>You can assign the proof as a homework exercise in\u00a0multivariable calculus.\u00a0Cavalieri&#8217;s principle\u00a0might be helpful.<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong>&nbsp;<br>Su, Francis E., et al. &#8220;Holey Beads.&#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>Take a bead 5 inches high, and bore a hole through it from north pole to south pole in such&#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":[20,7,3],"class_list":["post-263","page","type-page","status-publish","hentry","tag-analysis","tag-calculus","tag-easy"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/263","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=263"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/263\/revisions"}],"predecessor-version":[{"id":1471,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/263\/revisions\/1471"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=263"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}