Origami 4 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 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.
Table of contents :
I. Origami in Design and Art.
Paper Nautili: A Model for Three-Dimensional Planispiral Growth.
Curves and Flats.
The Celes Family of Modular Origami.
Fractal Crease Patterns.
Constructing Regular n-gonal Twist Boxes.
A Brief History of Oribotics.
Graphics Transformation of Origami Models.
One-Dimensional Origami: Polyhedral Skeletons in Dance.
II. Origami and Technology.
The Science of Miura-Ori: A Review.
Expandable Tubes with Negative Poisson’s Ratio and Their Application in Medicine.
Airbag Folding Based on Origami Mathematics.
III. Computational Origami.
Surface Transitions in Curved Origami.
The Method for Judging Rigid Foldability.
Simulation of Rigid Origami.
Facet Ordering and Crease Assignment in Uniaxial Bases.
Integer Programming Models for Flat Origami
Construction of 3D Virtual Origami Models from Sketches
An Excel-Based Solution to the One-Cut Folding Problem
Computer Origami Simulation and the Production of Origami Instructions
Recognition, Modeling, and Rendering Method for Origami Using 2D Bar Codes.
3D Origami Design Based on Tucking Molecules
eGami: Virtual Paperfolding and Diagramming Software.
Computational Origami System Eos
Computational Complexity of a Pop-Up Book
Concepts and Modeling of a Tessellated Molecule Surface
Folding Paper Shopping Bags
Origamic Architecture in the Cartesian Coordinate System
IV. Origami Mathematics
How Many Ways Can You Edge-Color a Cube?
Configuration Spaces for Flat Vertex Folds
One-, Two-, and Multi-Fold Origami Axioms
The Power of Multifolds: Folding the Algebraic Closure of the Rational Numbers
Fujimoto, Number Theory, and a New Folding Technique
On the Fish Base Crease Pattern and Its Flat Foldable Property
Orizuru Deformation Theory for Unbounded Quadrilaterals
A Crystal Map of the Orizuru World
A Geometrical Tree of Fortune Cookies
V. Origami in Education
Origametria: A Program to Teach Geometry and to Develop Learning Skills Using the Art of Origami
The Impact of Origami-Mathematics Lessons on Achievement and Spatial Ability of Middle-School Students
Understanding the Effect of Origami Practice, Cognition, and Language on Spatial Reasoning
Modular Origami in the Secondary Geometry Classroom
On the Effective Use of Origami in the Mathematics Classroom
Using Origami to Promote Problem Solving, Creativity, and Communication in Mathematics Education
Redundancy of Verbal Instructions in Origami Diagrams
Origami, Isometries, and Multilayer Tangram