{"id":413,"date":"2013-08-21T16:07:29","date_gmt":"2013-08-21T20:07:29","guid":{"rendered":"https:\/\/jasoncantarella.com\/wordpress\/?p=413"},"modified":"2013-08-21T16:07:29","modified_gmt":"2013-08-21T20:07:29","slug":"fold-and-cut-puzzles","status":"publish","type":"post","link":"https:\/\/jasoncantarella.com\/wordpress\/fold-and-cut-puzzles\/","title":{"rendered":"Fold And Cut Puzzles"},"content":{"rendered":"<p>Erik Demaine, Marty Demaine, and Anna Lubiw proved the following amazing thing a few years ago:<\/p>\n<ul>\n<li>You can fold a piece of paper so that ANY shape with straight edges can be cut out of the paper with a single cut.<\/li>\n<\/ul>\n<p>see\u00a0<a href=\"http:\/\/erikdemaine.org\/foldcut\/\" rel=\"nofollow\">Erik&#8217;s page on Fold-And-Cut problems<\/a>\u00a0to read more about the history of this fact. (Did you know that Betsy Ross cut out the five-pointed stars on the first American flag this way? I didn&#8217;t.) During (most of) the fall, I wrote some code with\u00a0<a href=\"http:\/\/www.cgal.org\/\" rel=\"nofollow\">CGAL<\/a>\u00a0and\u00a0<a href=\"http:\/\/www.wolfram.com\/\" rel=\"nofollow\">Mathematica<\/a>\u00a0to generate fold-and-cut creases.<\/p>\n<p>The resulting pictures made fun origami puzzles, so I&#8217;m posting them here for your amusement. Each of these images can be folded (along the creases shown) so that you can cut out the shaded letter with a single straight cut. You won&#8217;t need any &#8216;more&#8217; creases, but you might not use all of the creases shown. You only have to crease the dotted lines, not the outline of the letter or shape.\u00a0Can you do it?<\/p>\n<p><a href=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoU.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-thumbnail wp-image-416\" alt=\"DemoU\" src=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoU-150x150.png\" width=\"150\" height=\"150\" srcset=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoU-150x150.png 150w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoU-300x300.png 300w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoU-1024x1024.png 1024w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoU-904x904.png 904w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoU.png 1250w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/><\/a> <a href=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoG.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-thumbnail wp-image-417\" alt=\"DemoG\" src=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoG-150x150.png\" width=\"150\" height=\"150\" srcset=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoG-150x150.png 150w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoG-300x300.png 300w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoG-1024x1024.png 1024w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoG-904x904.png 904w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoG.png 1250w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/><\/a> <a href=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoA.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-thumbnail wp-image-418\" alt=\"DemoA\" src=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoA-150x150.png\" width=\"150\" height=\"150\" srcset=\"https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoA-150x150.png 150w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoA-300x300.png 300w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoA-1024x1024.png 1024w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoA-904x904.png 904w, https:\/\/jasoncantarella.com\/wordpress\/wp-content\/uploads\/2013\/08\/DemoA.png 1250w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/><\/a><\/p>\n<p>I suggest that you print out these PDF versions (<a href=\"https:\/\/jasoncantarella.com\/downloads\/DemoU.pdf\" rel=\"nofollow\">U<\/a>\u00a0<a href=\"https:\/\/jasoncantarella.com\/downloads\/DemoG.pdf\" rel=\"nofollow\">G<\/a>\u00a0<a href=\"https:\/\/jasoncantarella.com\/downloads\/DemoA.pdf\" rel=\"nofollow\">A<\/a>) and try it! Be sure to make the creases before you start folding.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Erik Demaine, Marty Demaine, and Anna Lubiw proved the following amazing thing a few years ago: You can fold a piece of paper so that ANY shape with straight edges can be cut out of the paper with a single cut. see\u00a0Erik&#8217;s page on Fold-And-Cut problems\u00a0to read more about the history of this fact. (Did [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,6],"tags":[],"class_list":["post-413","post","type-post","status-publish","format-standard","hentry","category-education","category-math"],"_links":{"self":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts\/413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/comments?post=413"}],"version-history":[{"count":1,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts\/413\/revisions"}],"predecessor-version":[{"id":419,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/posts\/413\/revisions\/419"}],"wp:attachment":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/media?parent=413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/categories?post=413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/tags?post=413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}