{"id":119353,"date":"2017-04-11T22:06:11","date_gmt":"2017-04-11T20:06:11","guid":{"rendered":"http:\/\/www.kraftfuttermischwerk.de\/blogg\/?p=119353"},"modified":"2017-04-11T22:08:41","modified_gmt":"2017-04-11T20:08:41","slug":"einen-1x1x1-wuerfel-in-ein-3x3x3-papier-einwickeln-ohne-das-gaenzlich-zerschneiden-zu-muessen","status":"publish","type":"post","link":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/einen-1x1x1-wuerfel-in-ein-3x3x3-papier-einwickeln-ohne-das-gaenzlich-zerschneiden-zu-muessen\/","title":{"rendered":"Einen 1x1x1 W\u00fcrfel in ein 3&#215;3 Papier einwickeln, ohne das g\u00e4nzlich zerschneiden zu m\u00fcssen"},"content":{"rendered":"<blockquote><p>Is it possible to wrap the cube with a 3\u00d73 piece of paper below it? Handling of the paper is subject to two conditions:<\/p>\n<p>1. The paper may be only cut or folded along the crease lines.<br \/>\n2. The cutting should not cause pieces to separate.<\/p><\/blockquote>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-11-2.jpg\" alt=\"\" width=\"600\" height=\"438\" class=\"aligncenter size-full wp-image-119354\" srcset=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-11-2.jpg 600w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-11-2-300x219.jpg 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><p>Gute Frage. Und ich war in Geometrie damals immer einer der besten.<\/p>\n<p>Wenn man das Papier zerschnippeln k\u00f6nnte, w\u00e4re die Frage keine schwierige. Was aber, wenn das Papier zum Umwickeln am St\u00fcck bleiben soll? Schwierige Frage.  <\/p>\n<p>L\u00f6sung: <!--more--><\/p>\n<p>There are three &#8222;cut-and-fold&#8220; operations: <\/p>\n<p>1.)<\/p>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-17.jpg\" alt=\"\" width=\"397\" height=\"394\" class=\"aligncenter size-full wp-image-119356\" srcset=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-17.jpg 397w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-17-150x150.jpg 150w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-17-300x298.jpg 300w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-17-136x136.jpg 136w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-17-100x100.jpg 100w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/>\n<p>2.) <\/p>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-15-1.jpg\" alt=\"\" width=\"358\" height=\"333\" class=\"aligncenter size-full wp-image-119357\" srcset=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-15-1.jpg 358w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-15-1-300x279.jpg 300w\" sizes=\"auto, (max-width: 358px) 100vw, 358px\" \/>\n<p>3.)<\/p>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-14-1.jpg\" alt=\"\" width=\"267\" height=\"331\" class=\"aligncenter size-full wp-image-119358\" srcset=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-14-1.jpg 267w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-14-1-242x300.jpg 242w\" sizes=\"auto, (max-width: 267px) 100vw, 267px\" \/>\n<p>This leads to a 3-step stair-like design. Place the cube on one of the middle squares:<\/p>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-13-2.jpg\" alt=\"\" width=\"263\" height=\"335\" class=\"aligncenter size-full wp-image-119359\" srcset=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-13-2.jpg 263w, https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-13-2-236x300.jpg 236w\" sizes=\"auto, (max-width: 263px) 100vw, 263px\" \/>\n<p>Now, fold the paper:<\/p>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-12-1.jpg\" alt=\"\" width=\"234\" height=\"271\" class=\"aligncenter size-full wp-image-119360\" \/>\n<p><a href=\"http:\/\/www.etudes.ru\/en\/\">Idee und L\u00f6sung von Mathematical Etudes<\/a>.<br \/>\n<small>(via <a href=\"http:\/\/boingboing.net\/2017\/04\/11\/can-we-wrap-a-1x1x1-cube-with.html\">BoingBoing<\/a>)<\/small><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Is it possible to wrap the cube with a 3\u00d73 piece of paper below it? Handling of the paper is subject to two conditions: 1.<\/p>\n<div class=\"more-link-wrapper\"><a class=\"more-link\" href=\"https:\/\/www.kraftfuttermischwerk.de\/blogg\/einen-1x1x1-wuerfel-in-ein-3x3x3-papier-einwickeln-ohne-das-gaenzlich-zerschneiden-zu-muessen\/\">Mehr lesen -&gt;<span class=\"screen-reader-text\">Einen 1x1x1 W\u00fcrfel in ein 3&#215;3 Papier einwickeln, ohne das g\u00e4nzlich zerschneiden zu m\u00fcssen<\/span><\/a><\/div>\n","protected":false},"author":1,"featured_media":119354,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[2481,3573,1190],"class_list":["post-119353","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nur-mal-so","tag-geometry","tag-math","tag-mind-fuck","entry"],"jetpack_featured_media_url":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-content\/uploads2\/2017\/04\/download-11-2.jpg","jetpack_shortlink":"https:\/\/wp.me\/pXEnA-v33","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/posts\/119353","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/comments?post=119353"}],"version-history":[{"count":10,"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/posts\/119353\/revisions"}],"predecessor-version":[{"id":119369,"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/posts\/119353\/revisions\/119369"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/media\/119354"}],"wp:attachment":[{"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/media?parent=119353"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/categories?post=119353"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kraftfuttermischwerk.de\/blogg\/wp-json\/wp\/v2\/tags?post=119353"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}