Math on the Street: 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>Origami as a Field of Mathematics</h3> <ul> <li>For a <a href="http://theory.lcs.mit.edu/~edemaine/photos/OSME_March2001/models/" target="_top">visual overview of the field of mathematical origami</a> see Erik Demaine's photos from the 3rd International Meeting of Origami Science, Math, and Education. <a href="http://www.merrimack.edu/~thull/osm/osm.html" target="_top">Abstracts</a> from this meeting can be found on Tom Hull's web page.<br><br></li> <li>Eric Weisstein's <a href="http://mathworld.wolfram.com/" target="_top">World of Mathematics</a> gives an <a href="http://mathworld.wolfram.com/Origami.html" target="_top">overview</a> of some results in mathematical origami.<br><br></li> <li><a href="http://www.merrimack.edu/~thull/OrigamiMath.html" target="_top">Tom Hull's mathematical origami page</a> is the most comprehensive source for information on mathematical origami that I have seen. The notes from his <a href="http://www.merrimack.edu/~thull/combgeom/combgeom.html" target="_top">Combinatorial Geometry class</a> survey many approaches to mathematical origami. Fields of mathematics invoked in Tom's course are convex polyhedral geometry (<a href="http://www.merrimack.edu/~thull/combgeom/graphnotes.html" target="_top">graph theory</a>), <a href="http://www.merrimack.edu/~thull/omfiles/geoconst.html" target="_top">Huzita's origami geometry axioms</a>, and combinatorial modelling of paper folding (<a href="http://www.merrimack.edu/~thull/combgeom/flatfold/flat.html" target="_top">flat folding</a>). Tom has also published a number of <a href="http://www.merrimack.edu/~thull/papers/papers.html" target="_top">mathematical origami papers</a>. To get a feel for the scope of the field of mathematical orgiami, you can browse through the abstracts from the <a href="http://www.merrimack.edu/~thull/osm/osm.html" target="_top">3rd International Meeting of Origami Science, Math, and Education</a> or Tom's <a href="http://www.merrimack.edu/~thull/oribib.html" target="_top">Origami Math Bibliography</a>.<br><br></li> <li><a href="http://www.langorigami.com/index.php4" target="_top">Robert Lang's web page</a> shows his many amazing origami designs and also discusses mathematical origami. You can also download his TreeMaker algorithm which can be used to design new origami bases.<br><br></li> <li><a href="http://www.math.lsu.edu/~verrill/origami/" target="_top">Helena Verrill</a> considers several mathematical origami questions on her web page: <a href="http://www.math.lsu.edu/~verrill/origami/tessellations/theory/" target="_top">classifying origami tessellations</a>, <a href="http://www.math.lsu.edu/~verrill/origami/sphere/" target="_top">folding spherical paper</a>, and <a href="http://www.math.lsu.edu/~verrill/origami/trisect" target="_top">origami trisection of an angle</a>.<br><br></li> <li> Koshiro shows how to use basic rules of origami construction to <a href="http://origami.gr.jp/People/CAGE_/divide/index-e.html" target="_top">divide a square paper</a> into arbitrarily many equal strips. This discussion includes proofs of several of Haga's theorems.<br><br></li> <li>Erik Demaine and Martin Demaine wrote a survey article, available in PDF format, that describes the field of <a href="http://db.uwaterloo.ca/~eddemain/papers/OSME2001/paper.pdf" target="_top">computational origami</a>. Erik's <a href="http://theory.lcs.mit.edu/~edemaine/folding/" target="_top">Folding and Unfolding Page</a> gives an overview of folding and unfolding problems with links to mathematical details and papers. Erik's primary interest is in finding algorithms that characterize foldability in different objects. The objects being folded range from paper, to robot arms, to proteins. See also Joe O'Rourke and Komei Fukada's page on <a href="http://compgeom.cs.uiuc.edu/~jeffe/open/unfold.html" target="_top"> unfolding convex polytopes</a>.<br><br></li> <li> Ivars Peterson wrote an article about <a href="http://www.maa.org/mathland/mathtrek_1_15_01.html" target="_top">flat folding and computational origami</a> also discussing applications of the field.<br><br></li> <li>David Wright discusses a connection between paper folding and the <a href="http://www.math.okstate.edu/mathdept/dynamics/lecnotes/node17.html" target="_top">fractal dragon curve</a>.<br><br></li> <li>David Eppstein, the founder of the <a href="http://www1.ics.uci.edu/~eppstein/junkyard/" target="_top">Geometry Junkyard</a>, has posted a mathematical bull session on the <a href="http://www1.ics.uci.edu/~eppstein/junkyard/napkin.html" target="_top">Margulis Napkin Problem</a>. This problem asks for a proof that it is impossible to fold a unit square to form a flat shape whose perimeter is greater than 4. In the course of the discussion, the participants realize that the problem is wrong as stated -- there is a way to fold a unit square to form a flat shape whose perimeter is greater than 4, and this turns out to be the key to creating many origami animals. <a href="http://www.math.lsu.edu/~verrill/origami/" target="_top">Helena Verrill</a> gives a clearer presentation of how to construct an <a href="http://www.math.lsu.edu/~verrill/origami/perimeter/" target="_top">origami counter-example</a>.<br><br></li> <li>David Eppstein's site hosted another mathematical bull session on the <a href="http://www1.ics.uci.edu/~eppstein/junkyard/teabag.html" target="_top">Teabag Problem</a>. This problem asks for the maximum volume a teabag can hold. A number of mathematicians contributed to the original discussion.<br><br></li>  <li>Roger Alperin defines and proves theorems about <a href="http://front.math.ucdavis.edu/math.HO/9912039" target="_top">Origami numbers</a>, numbers that are constructible by origami folds.<br><br></li> <li>Rick Nordal has a great page about <a href="http://www.geocities.com/snowflakegame/contents.html" target="_top">Einstein's Origami Snowflake Game</a>. This site includes many folding puzzles.<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>