Math on the Street: Applications of Mathematical Origami Links

<div id="SideBar"> <p align="center"> <a href="http://math.serenevy.net/?page=Home" target="_top"><img src="http://math.serenevy.net/Images/SmallLogo.gif" alt="Math on the Street" border=0 width=166 height=70></a> </p> <p><img src="http://math.serenevy.net/Images/RedDot.gif" alt="" height=8 width=8> <a href="http://math.serenevy.net/?page=About" target="_top">About the Project</a></p> <p><img src="http://math.serenevy.net/Images/RedDot.gif" alt="" height=8 width=8> <a href="http://math.serenevy.net/?page=Acknowledgments" target="_top">Acknowledgments</a></p> <p><img src="http://math.serenevy.net/Images/RedDot.gif" alt="" height=8 width=8> <a href="http://math.serenevy.net/?page=FunMath" target="_top">Fun Math Activities</a> <ul> <li><a href="http://math.serenevy.net/?page=OrigamiHome" target="_top">Origami</a></li> </ul> </p> </div>      <div id="Content"> <h1>Origami</h1> <center><table width="85%"><tr><td width="33%" align="center"><a href="http://math.serenevy.net/?page=OrigamiHome" class="button" target="_top">Polyhedra</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Figures" class="button" target="_top">Magic Pinwheel</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-WhereMath" class="button" target="_top">Where's The Math?</a></td></tr></table><table width="85%"><tr><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Challenge" class="button" target="_top">Challenge Problems</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Handouts" class="button" target="_top">Handouts</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Links" class="button" target="_top">Links</a></td></tr></table></center><center><hr width=80% /></center> <br> <h2>Links</h2> <ul> <a href="http://math.serenevy.net/?page=Origami-PolyhedraLinks" target="_top">Instructions for Making Origami Polyhedra</a><br> <a href="http://math.serenevy.net/?page=Origami-OtherFigureLinks" target="_top">Instructions for Making Other Origami Figures</a><br> <a href="http://math.serenevy.net/?page=Origami-ArtLinks" target="_top">Mathematics in Origami</a><br> <a href="http://math.serenevy.net/?page=Origami-TeachingLinks" target="_top">Using Origami to Teach Standard Mathematics Topics</a><br> <a href="http://math.serenevy.net/?page=Origami-MathLinks" target="_top">Origami as a Field of Mathematics</a><br> <a href="http://math.serenevy.net/?page=Origami-ApplicationLinks" target="_top">Applications of Mathematical Origami</a><br> <a href="http://math.serenevy.net/?page=Origami-SonobeHistoryLinks" target="_top">History of the Sonobe Module</a><br> </ul> <br><br><hr width="50%"><br><br> <h3>Applications of Mathematical Origami</h3> <ul> <li>The October 2001 Siam News article "In the Fold", available in PDF format, presents a <a href="http://www.siam.org/siamnews/10-01/origami.pdf" target="_top">range of applications of mathematical origami</a>.<br><br></li> <li><a href="http://www.progonos.com/furuti/" target="_top">Carlos A. Furuti</a> has a web site that explores distortions resulting from <a href="http://www.progonos.com/furuti/MapProj/CartIndex/cartIndex.html" target="_top">representing a spherical Earth as a flat map</a>. He also explores the virtues of a variety of polyhedral representations of the Earth and gives templates so that you can make your own origami polyhedral globes.<br><br></li> <li>Tom Hull wrote a paper, available as a PDF file, that discusses a <a href="http://www.merrimack.edu/~thull/papers/mapfold.pdf" target="_top">practical map fold</a> that allows a user viewing one small section to shift in any of the four cardinal directions without completely opening and refolding the map.<br><br></li> <li>Koryo Miura invented a widely celebrated procedure for folding a map called the <a href="http://www.britishorigami.org.uk/academic/miura.htm" target="_top">Miura-Ori fold</a> that is vastly superior to the conventional method. With his fold, a map opens and closes more easily and has less of a tendency to tear at folded corners. This method also has applications in other technologies, such as designing foldable solar sails. Olivier Boisard gives detailed directions for <a href="http://www.ec-lille.fr/~u3p/textang/pliage1a.html" target="_top">folding a Miura-Ori map</a>. Erik Demaine's photo collage from the 3rd International Meeting of Origami Science, Math, and Education includes some <a href="http://theory.lcs.mit.edu/~edemaine/photos/OSME_March2001/models/" target="_top">pictures</a> of the Miura-Ori map and a model of the solar sail unfolding in space. Under the "Space" link on their Think Quest origami site, Yuka Aihara, Sachiko Akikawa and Urara Akashi show some pictures of a <a href="http://library.thinkquest.org/28923/frame.html" target="_top">Japanese solar sail</a>, launched in 1995, that used the Miura-Ori fold.<br><br></li> <li>Lawrence Livermore National Laboratory is developing a number of <a href="http://www.llnl.gov/str/March03/Hyde.html" target="_top">foldable space telescopes</a>. SPACE.com's web site has an article with <a href="http://www.space.com/businesstechnology/technology/origami_design_020220-1.html" target="_top">additional information about the design of one of the telescopes</a>. Erik Demaine has some <a href="http://theory.lcs.mit.edu/~edemaine/photos/OSME_March2001/telescope/" target="_top">photos of a model of a folding telescope</a>.<br><br></li> <li>EASi Engineering GmbH used folding algorithms from origami to create a software system that tests the <a href="http://www.easi.de/products/ecfold/" target="_top">safety of airbag packings</a> for car manufacturers.<br><br></li> <li> A group at the Carnegie Mellon <a href="http://www.ri.cmu.edu/home.html" target="_top">Robotics Institute</a> has used origami theory to develop a <a href="http://www.ri.cmu.edu/projects/project_41.html" target="_top">sheet metal design system</a> for the <em>Intelligent Bending Workstation Project (IBW)</em>. The <a href="http://www.trumpf.com/3.index.html" target="_top">TRUMPF Group</a> also uses ideas from origami in their sheet metal designs. You can download an <a href="http://www.trumpf.com/3.img-cust/Sh_Metal_Chapter_10-Bending.pdf" target="_top">excerpt in PDF format from their book</a> <em>The Fascinating World of Sheet Metal</em> discussing connections to paper folding.<br><br></li> <li>Tomoko Fuse has a number of ideas for more efficient <a href="http://www1.zetosa.com.pl/~burczyk/osme/model80.jpg" target="_top">paper product designs</a> that are made from a single sheet of paper and use no adhesives. The designs are based on mathematical origami principles and the products can all be made by machines on a production line. <br><br></li> <li><a href="http://www.swiss.ai.mit.edu/users/radhi/" target="_top">Radhika Nagpal</a> is using ideas from biology and origami in the field of artificial intelligence. Radhika's <a href="http://www.swiss.ai.mit.edu/projects/amorphous/Progmat/" target="_top">thesis</a> presented a language for a self-organizing system that achieves global goals via local computations. The global language is based on <a href="http://www.merrimack.edu/~thull/omfiles/geoconst.html" target="_top">Huzita's axioms of geometric origami</a>, and the local instructions are inspired by developmental biology.<br><br></li> <li> A number of engineers combine origami with biomimetics (engineering that mimics mechanisms found in nature) to develop new technologies. The <a href="http://www-civ.eng.cam.ac.uk/dsl/" target="_top">Deployable Structures Laboratory</a> at the University of Cambridge has a number of projects relating to biomimetics and origami. <br><br></li> </ul> <div id="BottomBar"> <p /><hr> <img class="left" src="http://math.serenevy.net/Images/BWLogo.gif" alt="Math on the Street!" border=0 width="150" height="57"> <p class="about"> Last Updated: February 2003<br> <a href="http://math.serenevy.net/?page=Home" target="_top">http://math.serenevy.net/</a><br> Amanda Katharine Serenevy<br> <a href="mailto:viajera@bu.edu" target="_top">viajera@bu.edu</a><br> </p> </div> </div>