{"id":618,"date":"2011-02-22T18:57:55","date_gmt":"2011-02-23T01:57:55","guid":{"rendered":"http:\/\/www.glencora.org\/?p=618"},"modified":"2011-02-22T18:57:55","modified_gmt":"2011-02-23T01:57:55","slug":"topology-through-crochet","status":"publish","type":"post","link":"https:\/\/blogs.oregonstate.edu\/glencora\/2011\/02\/22\/topology-through-crochet\/","title":{"rendered":"Topology through crochet"},"content":{"rendered":"

\"crochetA good friend taught me how to crochet on Sunday night. \u00a0I started with the classic square-to-be-used-as-a-dish-rag project and moved onto the spiral-to-be-used-as-a-pot-stand project. Project number three? The M\u00f6bius Strip. Now, I understand the M\u00f6bius strip well. What kid has not taken a strip of paper, twisted it, taped the ends together and then drawn a line starting on one side of the paper only to seamlessly (or edge-lessly) reach the other side? I started crocheting the M\u00f6bius strip by creating a line and then joining the ends of the line, adding a twist to the line (a 1D M\u00f6bius strip?). I then continued crocheting along one edge of the cycle. But of course, since a M\u00f6bius strip\u00a0has only one boundary, I could continue extending the thickness of the strip by spiralling outwards.<\/p>\n

I thought: what would happen if I started dropping stitches, making this boundary shorter and shorter? Well, the M\u00f6bius strip is a non-orientable surface with one hole – that forms this boundary. I reminded myself that the M\u00f6bius strip is surface obtained by puncturing a projective plane – the non-orientable surface of minimum genus – however, I never had a good intuition of what the projective plane is. Let me tell you though, after dropping every fourth stitch on the boundary of my M\u00f6bius strip, I started having a pretty good idea of what a projective plane does.<\/p>\n

\"crochet<\/a>\"crochet<\/a>\"crochet<\/a><\/p>\n

I couldn’t continue until the boundary closed up – for obvious reasons – so I still have a M\u00f6bius strip, but the physical surface is close enough to the projective plane that I get a much better feel for what that means.<\/p>\n

I’m not the first person to crochet a M\u00f6bius strip – apparently it is a popular scarf design<\/a> – nor am I the first to explore geometry with crochet<\/a>. But I have to say that actually creating<\/em> this surface adds an intuition I’m not sure you could get elsewhere. Finally, if you haven’t seen Margaret Wertheim’s TED talk on math, crocheting and coral<\/a> including how to crochet a hyperbolic geometry and in which she says<\/p>\n

So here, in wool, through domestic feminine art, is the proof that the most famous postulate in mathematics is wrong.<\/p><\/blockquote>\n

I highly recommend it.<\/p>\n","protected":false},"excerpt":{"rendered":"

A good friend taught me how to crochet on Sunday night. \u00a0I started with the classic square-to-be-used-as-a-dish-rag project and moved onto the spiral-to-be-used-as-a-pot-stand project. Project number three? The M\u00f6bius Strip. Now, I understand the M\u00f6bius strip well. What kid has not taken a strip of paper, twisted it, taped the ends together and then drawn […]<\/p>\n","protected":false},"author":3747,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[106155,106190,106195],"class_list":["post-618","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-crochet","tag-tcs","tag-topology"],"_links":{"self":[{"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/posts\/618","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/users\/3747"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/comments?post=618"}],"version-history":[{"count":0,"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/posts\/618\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/media?parent=618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/categories?post=618"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/glencora\/wp-json\/wp\/v2\/tags?post=618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}