{"id":453,"date":"2019-06-28T16:11:01","date_gmt":"2019-06-28T16:11:01","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=453"},"modified":"2019-12-20T23:01:14","modified_gmt":"2019-12-20T23:01:14","slug":"rubber-bands-stuck-on-a-torus","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/rubber-bands-stuck-on-a-torus\/","title":{"rendered":"Rubber Bands Stuck on a Torus"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Consider a rubber tire (a torus) with a hole in it. Suppose that there is a green rubber band stuck to the outside of the torus that goes through the central cylinder, and a red rubber band pasted to the inside that stretches around the tire. So, if the tire were not there, the red and green rubber bands would be linked. <\/p>\n\n\n\n

Suppose now that the tire is turned inside out through the hole. This is a\u00a0continuous motion; so the red band is now on the outside, and the green on the inside. Moreover, it now seems as though the red and green rubber bands may be\u00a0unlinked<\/em>!<\/p>\n\n\n\n

How can this be?<\/p>\n\n\n\n

Presentation Suggestions:<\/strong>
Try this fun fact only if you can draw good pictures! Or, challenge students to try this with a physical model; try cutting and sewing ends of a sock.<\/p>\n\n\n\n

The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong>
You can resolve this paradox by actually turning the object inside out. What you find is that the red and blue rubber bands\u00a0switch<\/em>\u00a0locations; in other words, the red band now runs through the central cylinder rather than around it. So there is no\u00a0paradox; the rubber bands are still linked.<\/p>\n\n\n\n

Take a\u00a0topology\u00a0course for more fun!<\/p>\n\n\n\n

How to Cite this Page:<\/strong> 
Su, Francis E., et al. “Rubber Bands Stuck on a Torus.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n

Fun Fact suggested by: <\/strong>
Francis Su<\/p>\n","protected":false},"excerpt":{"rendered":"

Consider a rubber tire (a torus) with a hole in it. Suppose that there is a green rubber band stuck...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[4,12,18,11],"class_list":["post-453","page","type-page","status-publish","hentry","tag-medium","tag-other","tag-paradox","tag-topology"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/453","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=453"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/453\/revisions"}],"predecessor-version":[{"id":1618,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/453\/revisions\/1618"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=453"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}