{"id":10398,"date":"2015-11-20T11:13:39","date_gmt":"2015-11-20T16:13:39","guid":{"rendered":"https:\/\/web.uri.edu\/rinsfepscor\/?p=10398"},"modified":"2015-11-20T11:13:39","modified_gmt":"2015-11-20T16:13:39","slug":"10398","status":"publish","type":"post","link":"https:\/\/web.uri.edu\/rinsfepscor\/2015\/11\/20\/10398\/","title":{"rendered":"The mathematics of origami"},"content":{"rendered":"<h1><a href=\"https:\/\/web.uri.edu\/wp-content\/uploads\/sites\/848\/Robert-Lang.jpg\" rel=\"lightbox[10398]\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10403 size-full\" title=\"Origami artist and laser physicist Robert Lang speaking at Brown University Nov. 12, 2015\" src=\"https:\/\/web.uri.edu\/wp-content\/uploads\/sites\/848\/Robert-Lang.jpg\" alt=\"Robert Lang\" width=\"640\" height=\"381\" \/><\/a>In origami,\u00a0aesthetics meet application<\/h1>\n<p>Origami and mathematics seem like an odd pairing, but in the world <a href=\"http:\/\/www.langorigami.com\/\" target=\"_blank\">Robert J. Lang<\/a> inhabits, the two pursuits align not just to create stunning works of art, but also technological advances that can\u00a0deliver telescopes into space and life-saving drugs to targeted points inside the human body.<\/p>\n<p>Lang, a world-renowned origami artist and laser physicist, spoke to a packed Solomon Center audience at Brown University Thursday, Nov. 12. The <a href=\"https:\/\/icerm.brown.edu\/home\/index.php\" target=\"_blank\">Institute for Computational and Experimental Research in Mathematics<\/a> (ICERM)\u00a0and Rhode Island School of Design (RISD) <a href=\"http:\/\/naturelab.risd.edu\/\" target=\"_blank\">Edna Lawrence Nature Lab<\/a> co-hosted his lecture, From Flapping Birds to Space Telescopes: The Mathematics of Origami.<\/p>\n<p>The talk embodied the perfect juncture where art and design meet the science, technology, engineering, and math (STEM) fields, reinforcing the RISD-championed concept of <a href=\"http:\/\/stemtosteam.org\/\" target=\"_blank\">STEAM<\/a> \u2014\u00a0STEM plus Art \u2014 and leaving audience members awed by\u00a0the possibilities.<\/p>\n<blockquote><p>\u201cLook up in the sky.\u00a0You may or may not see origami. But, in the future, you will see origami looking back down at you.\u201d<\/p><\/blockquote>\n<p>Lang traced the history of the time-honored art and its method of folding a single piece of paper with two basic folds \u2014 valleys, which dip, and mountains, which ascend \u2014 into objects. The design of any origami object is encoded in the crease pattern, Lang explained, governed by rules that are fundamentally mathematic:<\/p>\n<ul>\n<li>2\u00a0colorability: A crease pattern is two colors; any touching regions must be different colors.<\/li>\n<li>The\u00a0number of folds always differs by 2: Mountain \u2013 valley = + or \u2013 2<\/li>\n<li>Alternate angles add up to a straight line<\/li>\n<li>Paper cannot intersect itself<\/li>\n<\/ul>\n<div style=\"float: right;width: 300px;background-color: #e0e8ff;border: 1px solid #999;padding: 10px;margin: 5px 10px 5px 20px\">\n<h3>The physicist artist<\/h3>\n<p>According to ICERM, Robert Lang is one of the foremost origami artists in the world and a pioneer in computational origami and the development of formal design algorithms for folding. He holds a Ph.D. in applied physics from Caltech, and during the course of work at NASA\/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored more 100 papers and 50 patents in lasers and optoelectronics. He also has authored, co-authored or edited 14 books and a CD-ROM on origami.<\/p>\n<p>Lang is a full-time artist and consultant on origami and its applications to engineering problems but continues his involvement in the world of lasers, most recently as the editor-in-chief of the IEEE Journal of Quantum Electronics from 2007-2010. He received Caltech&#8217;s highest honor, the Distinguished Alumni Award, in 2009 and was elected a Fellow of the American Mathematical Society in 2013.<\/p>\n<\/div>\n<p>\u201cEvery origami figure is nothing more than valley and mountain folds,\u201d said Lang, although the intricacies of the figures he presented \u2014 1,500 pleats to create the lifelike scales of a <a href=\"http:\/\/www.langorigami.com\/art\/gallery\/gallery.php?tag=reptiles-amphibians&amp;name=rattlesnake_1\" target=\"_blank\">rattlesnake<\/a> \u2014 defied such simplicity.<\/p>\n<p>The art of folding has been around for hundreds of years, Lang noted, but Akira Yoshizawa (1911- 2005), credited with inspiring a global renaissance of origami, created a language to convey the process.<\/p>\n<p>\u201cOnce you understood the language, how to fold origami shapes, once you could communicate, you could build upon it,\u201d said Lang. \u201cThis ability to grow and share kicked off exponential growth.\u201d<\/p>\n<p>Origami went from flapping birds and cootie catchers to <a href=\"http:\/\/www.langorigami.com\/art\/gallery\/gallery.php?tag=mythical&amp;name=assyrian_bull\" target=\"_blank\">mind-blowing figures<\/a>\u00a0with such precise details as cloven hoofs and insect pincers.\u00a0What had been static for hundreds of years soon saw thousands of new designs. And although his artist friends don\u2019t like the inference, Lang said, when math came to origami, the field transformed. Everyone \u2014 artists and mathematicians alike \u2014 began using mathematical concepts to <a href=\"http:\/\/www.langorigami.com\/art\/compositions\/compositions.php\" target=\"_blank\">engineer designs<\/a>.<\/p>\n<p>Using pleats to create texture, based on mathematical repeating patterns, had the greatest impact on origami, according to Lang, who wrote a computer program, <a href=\"http:\/\/www.langorigami.com\/science\/computational\/treemaker\/treemaker.php\" target=\"_blank\">TreeMaker<\/a>, that can solve equations simultaneously and spit out a crease pattern.<\/p>\n<p>The slide of an origami cactus Lang created \u2014 <a href=\"http:\/\/www.langorigami.com\/art\/gallery\/gallery.php?name=cactus\" target=\"_blank\">a green plant in a red pot<\/a> \u2014 drew gasps from the audience when he noted that the two-colored figure sprung from just one sheet of paper. He also showed a <a href=\"http:\/\/www.langorigami.com\/art\/gallery\/gallery.php?tag=arthropods\" target=\"_blank\">series of bugs<\/a>, each one more intricate than the one before, a so-called bug war of increasing complexity.<\/p>\n<p>At the same time, these design capabilities are unleashing previously unimagined potential in exploration and discovery.<\/p>\n<p>A telescope lens the size of a football field needs to be launched into space. Through origami, the lens can be folded \u201csmall for the journey and large for the destination,\u201d said Lang. Or, for more recreational pursuits, think of <a href=\"http:\/\/www.orukayak.com\/\">a kayak folded up<\/a> for easy transport and then unfolded for use.<\/p>\n<p>The same theory applies in medicine. Lang reeled off a list \u2014 an implant that unfolds from a delivery tube, an origami heart stent, and a box that unfolds and releases an anti-cancer drug.<\/p>\n<p>\u201cHow small can we go?\u201d Lang asked. \u201cThe laws of folding can apply to paper or to molecules \u2026 at any scale.\u201d<\/p>\n<p>There is self-folding using light absorption and hydrogel programmed folding, swelling or unfolding in response to temperature change. <a href=\"https:\/\/www.nasa.gov\/\" target=\"_blank\">NASA<\/a>, too, is developing methods of origami applications in space.<\/p>\n<p>\u201cLook up in the sky,\u201d Lang urged the audience as he closed out his talk. \u201cYou may or may not see origami. But, in the future, you will see origami looking back down at you.\u201d<\/p>\n<p style=\"text-align: right\"><em>Story and photo by Amy Dunkle<\/em><\/p>\n<div class=\"oembed oembed-youtube-com\" style=\"\" data-url=\"https:\/\/www.youtube.com\/watch?v=NYKcOFQCeno\"><iframe loading=\"lazy\" width=\"1000\" height=\"563\" src=\"https:\/\/www.youtube.com\/embed\/NYKcOFQCeno?feature=oembed\" frameborder=\"0\" allow=\"autoplay; encrypted-media\" allowfullscreen><\/iframe><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In origami,\u00a0aesthetics meet application Origami and mathematics seem like an odd pairing, but in the world Robert J. Lang inhabits, the two pursuits align not just to create stunning works of art, but also technological advances that can\u00a0deliver telescopes into space and life-saving drugs to targeted points inside the human body. Lang, a world-renowned origami [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[21,1],"tags":[237,336,393,489,594],"class_list":["post-10398","post","type-post","status-publish","format-standard","hentry","category-news","category-uncategorized","tag-edna-lawrence-nature-lab","tag-icerm","tag-mathematics","tag-origami","tag-robert-lang"],"acf":[],"_links":{"self":[{"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/posts\/10398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/comments?post=10398"}],"version-history":[{"count":0,"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/posts\/10398\/revisions"}],"wp:attachment":[{"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/media?parent=10398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/categories?post=10398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/web.uri.edu\/rinsfepscor\/wp-json\/wp\/v2\/tags?post=10398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}