{"id":2581,"date":"2025-08-21T15:00:16","date_gmt":"2025-08-21T19:00:16","guid":{"rendered":"https:\/\/www.wayneprecht.org\/blogs\/readings\/?p=2581"},"modified":"2025-08-21T15:00:17","modified_gmt":"2025-08-21T19:00:17","slug":"geek-fun-the-klien-bottle","status":"publish","type":"post","link":"https:\/\/www.wayneprecht.org\/blogs\/readings\/?p=2581","title":{"rendered":"Geek Fun – The Klien Bottle"},"content":{"rendered":"\n

I’ve always had a fascination with math, including most of its subdisciplines. I’m not very good at it; my undergrad career suggested CS was a much wiser choice than physics, even if we didn’t get to play with lasers.<\/p>\n\n\n\n

I guess I am much better than the typical non-STEM person; I can make change without help and calculate a tip in my head. Evidence suggests these are vanishing skills. And I can’t think of anyone (else) who would buy a couple of used calculus books to self-study DEs so I could decode the equations in a physics book.<\/p>\n\n\n\n

One really cool area that most people can appreciate, even if the details might give them a headache, is topology. Cut a 1″ wide strip off a piece of paper, flip ONE end over, and tape it together. You’ve created a M\u00f6bius strip: a bounded, one-sided, nonorientable surface.<\/p>\n\n\n

\n
\"M\u00f6bius<\/a>
M\u00f6bius Strip By David Benbennick (Wikipedia)<\/figcaption><\/figure>\n<\/div>\n\n\n

If you trace along its length with a pencil, you will come back to the starting point without lifting the pencil. It seems like it has two sides, but it does not. Non-orientable means there’s no way to distinguish between clockwise and counterclockwise. The recycling symbol is an example. Bounded means it has an edge. In this case, exactly one. A sphere is an example of an unbounded object.<\/p>\n\n\n\n

As cool as a M\u00f6bius strip is, you can make something even cooler if you connect two M\u00f6bius strips edge to edge. Now you have a one-sided object with no boundary. Well, actually, you have a 3D representation of a Klien bottle, a proper one does not self-intersect, but you need four dimensions to make that work\u2026<\/p>\n\n\n

\n
\"Klein<\/a>
Klein Bottle By Tttrung (Wikipedia)<\/figcaption><\/figure>\n<\/div>\n\n\n

I told you it was deeply nerdy. Look, I am sparing you any equations or discussion of manifolds\u2026<\/p>\n\n\n\n


Anyway, there’s a Stanford mathematics professor (Cliff Stoll) who figured out how to produce these out of glass. He got a company to make an order of them, and he sells them as the ultimate math geek gift. I saw it and had to have one. So, I ordered one.<\/p>\n\n\n\n

Even though it technically has zero volume, you can fill it with water. But it’s not easy. Nor is drying it out\u2026<\/p>\n\n\n

\n
\"Pyrex<\/a>
Pyrex Klien Bottle<\/figcaption><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"

I’ve always had a fascination with math, including most of its subdisciplines. I’m not very good at it; my undergrad career suggested CS was a much wiser choice than physics, Continue Reading →<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[235],"tags":[250,249],"class_list":["post-2581","post","type-post","status-publish","format-standard","hentry","category-life-adventures","tag-klien-bottle","tag-mathematics"],"_links":{"self":[{"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=\/wp\/v2\/posts\/2581","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2581"}],"version-history":[{"count":1,"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=\/wp\/v2\/posts\/2581\/revisions"}],"predecessor-version":[{"id":2582,"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=\/wp\/v2\/posts\/2581\/revisions\/2582"}],"wp:attachment":[{"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayneprecht.org\/blogs\/readings\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}