{"id":477,"date":"2019-06-29T21:58:34","date_gmt":"2019-06-29T21:58:34","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=477"},"modified":"2019-12-11T17:06:46","modified_gmt":"2019-12-11T17:06:46","slug":"pretzel-unlinking","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/pretzel-unlinking\/","title":{"rendered":"Pretzel Unlinking"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Imagine that each of the ropes in the two sets of links in Figure 1 are solid (with thickness) and made of very flexible and stretchy rubber.<\/p>\n\n\n\n

Question: is it possible to deform one set of links into the other in a continuous motion (without tearing or cutting)? In other words, can you get the purple pretzel off the red ring?<\/p>\n\n\n\n

Surprise answer: Yes!!<\/p>\n\n\n\n

Presentation Suggestions:<\/strong>
Students (as well as you) may find this very hard to believe!<\/p>\n\n\n\n

The Math Behind the Fact:<\/strong>
The transformation can best be explained by a sequence of pictures that demonstrate the transformation, since it is not easy to describe in words! It is important here that the ropes are solid, with thickness, and very stretchy; it wouldn’t be possible otherwise. See Unbelievable Unlinking<\/a> for a hint on how it can be done. The reference contains a solution.<\/p>\n\n\n\n

A course in topology<\/a><\/em> is the best place to learn about links and knots and continuous deformations.<\/p>\n\n\n\n

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

References:<\/strong>
V.V. Prasalov, Intuitive Topology<\/a><\/em>.<\/p>\n\n\n\n

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

Imagine that each of the ropes in the two sets of links in Figure 1 are solid (with thickness) and...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,6,4,12,11],"class_list":["post-477","page","type-page","status-publish","hentry","tag-easy","tag-hard","tag-medium","tag-other","tag-topology"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/477","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=477"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/477\/revisions"}],"predecessor-version":[{"id":1579,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/477\/revisions\/1579"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=477"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}