Skip to Content

Origami 4

Edited by Robert J. Lang

A K Peters/CRC Press – 2009 – 570 pages

Purchasing Options:

  • Add to CartPaperback: $89.95
    August 5th 2009


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.


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


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

Author Bio

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.

Name: Origami 4 (Paperback)A K Peters/CRC Press 
Description: Edited by Robert J. Lang. 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...
Categories: Mathematics & Statistics, Geometry, Foundations & Theorems