{"id":213,"date":"2022-12-08T18:39:01","date_gmt":"2022-12-08T18:39:01","guid":{"rendered":"https:\/\/yingster.net\/blog\/?p=213"},"modified":"2022-12-08T18:41:12","modified_gmt":"2022-12-08T18:41:12","slug":"klein-bottles","status":"publish","type":"post","link":"https:\/\/yingster.net\/blog\/2022\/12\/08\/klein-bottles\/","title":{"rendered":"Klein Bottles"},"content":{"rendered":"<p>A <a href=\"https:\/\/en.wikipedia.org\/wiki\/Klein_bottle\">Klein bottle<\/a> is like a Mobius strip, but is not bounded. It&#8217;s a manifold (meaning has no holes) surface with only 1 side. While you can&#8217;t technically create this object in 3D space, you can cheat by having a self-intersecting point. It&#8217;s a fun thing for people who are interested in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Topology\">topology<\/a>.<\/p>\n<p>I&#8217;m not a mathematician, but I enjoy learning about mathematical concepts. Over the years I&#8217;ve seen the Klein bottle come up from time to time, especially the glass representation created by Cliff Stoll. I remember first hearing about him in a video that was showcasing his under-house storage solution for his many glass Klein bottles that he sells.<\/p>\n<p><iframe loading=\"lazy\" title=\"The man with 1,000 Klein Bottles UNDER his house - Numberphile\" width=\"660\" height=\"371\" src=\"https:\/\/www.youtube.com\/embed\/-k3mVnRlQLU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>I decided to buy one for myself. I had heard that the buying process was first rate, and that was no exaggeration.<\/p>\n<p>Cliff himself emailed me to let me know the bottle was being shipped. Not only did he include a personalized, and very humorous letter, he included many photos of the very bottle I would be receiving!<\/p>\n<p><a href=\"http:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-2022-12-02-at-11.21.04-AM.png\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-215 size-medium\" src=\"http:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-2022-12-02-at-11.21.04-AM-300x183.png\" alt=\"\" width=\"300\" height=\"183\" srcset=\"https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-2022-12-02-at-11.21.04-AM-300x183.png 300w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-2022-12-02-at-11.21.04-AM-768x468.png 768w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-2022-12-02-at-11.21.04-AM.png 869w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-216 aligncenter\" src=\"http:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/DSCN4217-300x225.jpeg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/DSCN4217-300x225.jpeg 300w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/DSCN4217-1024x768.jpeg 1024w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/DSCN4217-768x576.jpeg 768w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/DSCN4217.jpeg 1280w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>After just a couple of days, my parcel arrived!<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"size-medium wp-image-219 aligncenter\" src=\"http:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/image0-300x225.jpeg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/image0-300x225.jpeg 300w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/image0-1024x768.jpeg 1024w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/image0-768x576.jpeg 768w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/image0-1536x1152.jpeg 1536w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/image0-rotated.jpeg 1544w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>It included invoices, inspection paperwork, &#8220;topological propaganda,&#8221; instructions, an advertisement, and stickers. Each page is packed to the brim with mathematical humor, jokes, puns, and more. I couldn&#8217;t stop smiling as I read through it all.<\/p>\n<p><a href=\"http:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Paperwork.png\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-223 size-medium\" src=\"http:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Paperwork-300x223.png\" alt=\"\" width=\"300\" height=\"223\" srcset=\"https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Paperwork-300x223.png 300w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Paperwork-1024x762.png 1024w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Paperwork-768x572.png 768w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Paperwork-1536x1143.png 1536w, https:\/\/yingster.net\/blog\/wp-content\/uploads\/2022\/12\/Paperwork.png 1933w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>I can&#8217;t recommend getting one enough. It&#8217;s an fascinating object created by an interesting person! Thank you Cliff for this exceptional experience!<\/p>\n<p><a href=\"https:\/\/www.kleinbottle.com\/\">https:\/\/www.kleinbottle.com\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Klein bottle is like a Mobius strip, but is not bounded. It&#8217;s a manifold (meaning has no holes) surface with only 1 side. While you can&#8217;t technically create this object in 3D space, you can cheat by having a self-intersecting point. It&#8217;s a fun thing for people who are interested in topology. I&#8217;m not &hellip; <a href=\"https:\/\/yingster.net\/blog\/2022\/12\/08\/klein-bottles\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Klein Bottles<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[5,7],"tags":[],"_links":{"self":[{"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/posts\/213"}],"collection":[{"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/comments?post=213"}],"version-history":[{"count":6,"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/posts\/213\/revisions"}],"predecessor-version":[{"id":226,"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/posts\/213\/revisions\/226"}],"wp:attachment":[{"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/media?parent=213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/categories?post=213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/yingster.net\/blog\/wp-json\/wp\/v2\/tags?post=213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}