Origami 4 Fourth International Meeting of Origami Science, Mathematics, and Education

The connections between origami, mathematics, science, technology, and education have been a topic of considerable interest now for several decades. While many individuals have happened upon discrete connections among these fields during the twentieth century, the field really took off when previously isolated individuals began to make stronger connections with each other through a series of conferences exploring the links between origami and "the outside world." The Fourth International Meeting on Origami in Science, Mathematics, and Education (4OSME), held in September, 2006, at the California Institute of Technology in Pasadena, California, brought together an unprecedented number of researchers presenting on topics ranging from mathematics, to technology, to educational uses of origami, to fine art, and to computer programs for the design of origami. Selected papers based on talks presented at that conference make up the book you hold in your hands.

Origami in Design and ArtPaper Nautili: A Model for Three-Dimensional Planispiral GrowthArle LommelCurves and FlatsSaadya SternbergThe Celes Family of Modular OrigamiMiyuki KawamuraFractal Crease PatternsUshio IkegamiConstructing Regular n-gonal Twist Boxessarah-marie belcastro and Tamara VeenstraA Brief History of OriboticsMatthew GardinerGraphics Transformation of Origami ModelsL. I. ZamiatinaOne-Dimensional Origami: Polyhedral Skeletons in DanceKarl SchafferOrigami and TechnologyThe Science of Miura-Ori: A ReviewKoryo MiuraOrigami-Inspired Self-AssemblyGalen T. PickettExpandable Tubes with Negative Poisson’s Ratio and Their Application in MedicineZhong You and Kaori KuribayashiAirbag Folding Based on Origami MathematicsChristoffer Cromvik and Kenneth ErikssonComputational OrigamiSurface Transitions in Curved OrigamiJeannine MoselyFolding CurvesRobert GeretschlagerThe Method for Judging Rigid FoldabilityNaohiko Watanabe and Ken-ichi KawaguchiSimulation of Rigid OrigamiTomohiro TachiFacet Ordering and Crease Assignment in Uniaxial BasesRobert J. Lang and Erik D. DemaineInteger Programming Models for Flat OrigamiGoran KonjevodConstruction of 3D Virtual Origami Models from SketchesHiroshi Shimanuki, Jien Kato, and Toyohide WatanabeAn Excel-Based Solution to the One-Cut Folding ProblemAlexander C. HuangComputer Origami Simulation and the Production of Origami InstructionsTung Ken LamRecognition, Modeling, and Rendering Method for Origami Using 2D Bar CodesJun Mitani3D Origami Design Based on Tucking MoleculesTomohiro TachieGami: Virtual Paperfolding and Diagramming SoftwareJack FastagComputational Origami System EosTetsuo Ida, Hidekazu Takahashi, Mircea Marin, Asem Kasem, and Fadoua GhourabiComputational Complexity of a Pop-Up BookRyuhei Uehara and Sachio TeramotoConcepts and Modeling of a Tessellated Molecule SurfaceElias HalloranFolding Paper Shopping BagsDevin J. Balkcom, Erik D. Demaine, Martin L. Demaine, John A. Ochsendorf, and Zhong YouOrigamic Architecture in the Cartesian Coordinate SystemChew Min Cheong, Hajijubok Zainodin, and Hiromasa SuzukiOrigami MathematicsHow Many Ways Can You Edge-Color a Cube?Charlene MorrowConfiguration Spaces for Flat Vertex FoldsThomas C. HullOne-, Two-, and Multi-Fold Origami AxiomsRoger C. Alperin and Robert J. LangThe Power of Multifolds: Folding the Algebraic Closure of the Rational NumbersTimothy Y. Chow and C. Kenneth FanFujimoto, Number Theory, and a New Folding TechniqueTamara B. VeenstraOn the Fish Base Crease Pattern and Its Flat Foldable PropertyHideaki AzumaOrizuru Deformation Theory for Unbounded QuadrilateralsToshikazu Kawasaki and Hidefumi KawasakiA Crystal Map of the Orizuru WorldToshikazu KawasakiA Geometrical Tree of Fortune CookiesJun MaekawaOrigami in EducationOrigametria: A Program to Teach Geometry and to Develop LearningSkills Using the Art of OrigamiMiri Golan and Paul JacksonThe Impact of Origami-Mathematics Lessons on Achievement and Spatial Ability of Middle-School StudentsNorma J. BoakesUnderstanding the Effect of Origami Practice, Cognition, and Language on Spatial ReasoningMichael Wilson, Robin Flanagan, Rona Gurkewitz, and Laura Skrip Modular Origami in the Secondary Geometry ClassroomMargaret CagleOn the Effective Use of Origami in the Mathematics ClassroomV’Ann Cornelius and Arnold TubisUsing Origami to Promote Problem Solving, Creativity, and Communication in Mathematics EducationSue Pope and Tung Ken LamRedundancy of Verbal Instructions in Origami DiagramsKoichi TateishiOrigami, Isometries, and Multilayer TangramEmma Frigerio

An avid student of origami for more than 40 years, Robert J. Lang is regarded as a leading master of the art, with over 500 designs catalogued and diagrammed. Following a successful career as a physicist and engineer, during which he authored or coauthored over 80 papers and 50 patents awarded and pending on lasers, optoelectronics, folding, and computational origami, he is now a full-time origami artist.Lang's work combines aspects of the Western school of mathematical origami design with the Eastern emphasis on line and form to yield models distinctive, elegant, and challenging to fold. His work has been shown in New York's Museum of Modern Art; Paris's Carrousel du Louvre; the Peabody Essex Museum, in Salem, Massachusetts; San Diego's Mingei International Museum; and the Nippon Origami Museum, in Kaga, Japan, among others. In 1992, Lang became the first Westerner invited to address the Nippon Origami Association's annual meeting, and he has been an invited guest at international origami conventions around the world.A pioneer of the cross-disciplinary marriage of origami with mathematics, Lang has been one of the few Western columnists for Origami Tanteidan Magazine, the journal of the Japan Origami Academic Society. He is the author or coauthor of nine books and has consulted on applying origami to engineering problems ranging from air-bag design to expandable space telescopes. He is a fellow of the Optical Society of America, a member of the IEEE Photonics Society, and editor in chief of the IEEE Journal of Quantum Electronics.