572 Pages
    by A K Peters/CRC Press

    572 Pages
    by A K Peters/CRC Press

    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 Art
    Paper Nautili: A Model for Three-Dimensional Planispiral Growth
    Arle Lommel
    Curves and Flats
    Saadya Sternberg
    The Celes Family of Modular Origami
    Miyuki Kawamura
    Fractal Crease Patterns
    Ushio Ikegami
    Constructing Regular n-gonal Twist Boxes
    sarah-marie belcastro and Tamara Veenstra
    A Brief History of Oribotics
    Matthew Gardiner
    Graphics Transformation of Origami Models
    L. I. Zamiatina
    One-Dimensional Origami: Polyhedral Skeletons in Dance
    Karl Schaffer

    Origami and Technology
    The Science of Miura-Ori: A Review
    Koryo Miura
    Origami-Inspired Self-Assembly
    Galen T. Pickett
    Expandable Tubes with Negative Poisson’s Ratio and Their Application in Medicine
    Zhong You and Kaori Kuribayashi
    Airbag Folding Based on Origami Mathematics
    Christoffer Cromvik and Kenneth Eriksson

    Computational Origami
    Surface Transitions in Curved Origami
    Jeannine Mosely
    Folding Curves
    Robert Geretschlager
    The Method for Judging Rigid Foldability
    Naohiko Watanabe and Ken-ichi Kawaguchi
    Simulation of Rigid Origami
    Tomohiro Tachi
    Facet Ordering and Crease Assignment in Uniaxial Bases
    Robert J. Lang and Erik D. Demaine
    Integer Programming Models for Flat Origami
    Goran Konjevod
    Construction of 3D Virtual Origami Models from Sketches
    Hiroshi Shimanuki, Jien Kato, and Toyohide Watanabe
    An Excel-Based Solution to the One-Cut Folding Problem
    Alexander C. Huang
    Computer Origami Simulation and the Production of Origami Instructions
    Tung Ken Lam
    Recognition, Modeling, and Rendering Method for Origami Using 2D Bar Codes
    Jun Mitani
    3D Origami Design Based on Tucking Molecules
    Tomohiro Tachi
    eGami: Virtual Paperfolding and Diagramming Software
    Jack Fastag
    Computational Origami System Eos
    Tetsuo Ida, Hidekazu Takahashi, Mircea Marin, Asem Kasem, and Fadoua Ghourabi
    Computational Complexity of a Pop-Up Book
    Ryuhei Uehara and Sachio Teramoto
    Concepts and Modeling of a Tessellated Molecule Surface
    Elias Halloran
    Folding Paper Shopping Bags
    Devin J. Balkcom, Erik D. Demaine, Martin L. Demaine, John A. Ochsendorf, and Zhong You
    Origamic Architecture in the Cartesian Coordinate System
    Chew Min Cheong, Hajijubok Zainodin, and Hiromasa Suzuki

    Origami Mathematics
    How Many Ways Can You Edge-Color a Cube?
    Charlene Morrow
    Configuration Spaces for Flat Vertex Folds
    Thomas C. Hull
    One-, Two-, and Multi-Fold Origami Axioms
    Roger C. Alperin and Robert J. Lang
    The Power of Multifolds: Folding the Algebraic Closure of the Rational Numbers
    Timothy Y. Chow and C. Kenneth Fan
    Fujimoto, Number Theory, and a New Folding Technique
    Tamara B. Veenstra
    On the Fish Base Crease Pattern and Its Flat Foldable Property
    Hideaki Azuma
    Orizuru Deformation Theory for Unbounded Quadrilaterals
    Toshikazu Kawasaki and Hidefumi Kawasaki
    A Crystal Map of the Orizuru World
    Toshikazu Kawasaki
    A Geometrical Tree of Fortune Cookies
    Jun Maekawa

    Origami in Education
    Origametria: A Program to Teach Geometry and to Develop Learning
    Skills Using the Art of Origami
    Miri Golan and Paul Jackson
    The Impact of Origami-Mathematics Lessons on Achievement and Spatial Ability of Middle-School Students
    Norma J. Boakes
    Understanding the Effect of Origami Practice, Cognition, and Language on Spatial Reasoning
    Michael Wilson, Robin Flanagan, Rona Gurkewitz, and Laura Skrip
    Modular Origami in the Secondary Geometry Classroom
    Margaret Cagle
    On the Effective Use of Origami in the Mathematics Classroom
    V’Ann Cornelius and Arnold Tubis
    Using Origami to Promote Problem Solving, Creativity, and Communication in Mathematics Education
    Sue Pope and Tung Ken Lam
    Redundancy of Verbal Instructions in Origami Diagrams
    Koichi Tateishi
    Origami, Isometries, and Multilayer Tangram
    Emma 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.

    These 46 diverse, first-class articles give the field a fabulous overview and offer invaluable citations, particularly to Internet resources. In particular. R. C. Alperin and R. J. Lang's 'One-, Two-, and Multi-Fold Origami Axioms' and T. Y. Chow and C. K. Fan's 'The Power of Multifolds' together make a fascinating contemporary foil to any examination of classical ruler-and-compass constructions in a geometry or Galois theory course. Highly recommended.
    —D. V. Feldman, CHOICE, June 2010

    Origami is an unusual area of mathematics in that it is as much an art form as it is mathematics and very young children can be exposed to and enthralled by it. The breadth of structures that can be made by folding paper is substantial and expanding all the time. This book is a mathematical examination and explanation of origami; it is a collection of research papers written by some of the experts in the field.
    —Charles Ashbacher, The Mathematical Association of America, December 2009

    Fantastic book! It will create new folds in your brain whether you are an artist, scientist, inventor, educator, or simply like to be amazed. The balance between mathematical theory and manipulative practice, and between artistic and educational applications makes this a book for everyone. I look forward to using this book personally and professionally.
    —Robert Root-Bernstein, Ph. D., co-author of Sparks of Genius, June 2009

    copy of Origami 4 just arrived!! Wow, I have just flipped through it, and for now this is the book I would take with me on a deserted island. Instead I need to finish getting ready for our local meeting tomorrow night, teaching at a retirement home on Friday, and teaching during a Girl Scout Alumni Campout this weekend. The cover is shiny and slick, in color, and the binding seems sturdy for all 560 pages of the book. The center stays open by itself, and closer to the covers, not much pressure is needed to keep it open. The spine margins allow the page to be read, without breaking the spine. The pages are well printed, with good B&W contrast. Sadly, no color inside. We have been spoiled with color. It is helpful, but truly not necessary. It is a great book, thanks to all who submitted articles, and to Robert Lang for editing.
    —Kathy Knapp, Founder of OPA (Origami Peoria Area), September 2009