Origami 4 (Origami (AK Peters))

Contents......Page 6
Preface......Page 10
I. Origami in Design and Art......Page 14
Paper Nautili: A Model for Three-Dimensional Planispiral Growth......Page 16
Curves and Flats......Page 22
The Celes Family of Modular Origami......Page 34
Fractal Crease Patterns......Page 44
Constructing Regular n-gonal Twist Boxes......Page 54
A Brief History of Oribotics......Page 64
Graphics Transformation of Origami Models......Page 74
One-Dimensional Origami: Polyhedral Skeletons in Dance......Page 88
II. Origami and Technology......Page 98
The Science of Miura-Ori: A Review......Page 100
Origami-Inspired Self-Assembly......Page 114
Expandable Tubes with Negative Poisson’s Ratio and Their Application in Medicine......Page 130
Airbag Folding Based on Origami Mathematics......Page 142
III. Computational Origami......Page 154
Surface Transitions in Curved Origami......Page 156
Folding Curves......Page 164
The Method for Judging Rigid Foldability......Page 178
Simulation of Rigid Origami......Page 188
Facet Ordering and Crease Assignment in Uniaxial Bases......Page 202
Integer Programming Models for Flat Origami......Page 220
Construction of 3D Virtual Origami Models from Sketches......Page 230
An Excel-Based Solution to the One-Cut Folding Problem......Page 242
Computer Origami Simulation and the Production of Origami Instructions......Page 250
Recognition, Modeling, and Rendering Method for Origami Using 2D Bar Codes......Page 264
3D Origami Design Based on Tucking Molecules......Page 272
eGami: Virtual Paperfolding and Diagramming Software......Page 286
Computational Origami System Eos......Page 298
Computational Complexity of a Pop-Up Book......Page 308
Concepts and Modeling of a Tessellated Molecule Surface......Page 318
Folding Paper Shopping Bags......Page 328
Origamic Architecture in the Cartesian Coordinate System......Page 348
IV. Origami Mathematics......Page 362
How Many Ways Can You Edge-Color a Cube?......Page 364
Configuration Spaces for Flat Vertex Folds......Page 374
One-, Two-, and Multi-Fold Origami Axioms......Page 384
The Power of Multifolds: Folding the Algebraic Closure of the Rational Numbers......Page 408
Fujimoto, Number Theory, and a New Folding Technique......Page 418
On the Fish Base Crease Pattern and Its Flat Foldable Property......Page 430
Orizuru Deformation Theory for Unbounded Quadrilaterals......Page 440
A Crystal Map of the Orizuru World......Page 452
A Geometrical Tree of Fortune Cookies......Page 462
V. Origami in Education......Page 470
Origametria: A Program to Teach Geometry and to Develop Learning Skills Using the Art of Origami......Page 472
The Impact of Origami-Mathematics Lessons on Achievement and Spatial Ability of Middle-School Students......Page 484
Understanding the Effect of Origami Practice, Cognition, and Language on Spatial Reasoning......Page 496
Modular Origami in the Secondary Geometry Classroom......Page 510
On the Effective Use of Origami in the Mathematics Classroom......Page 520
Using Origami to Promote Problem Solving, Creativity, and Communication in Mathematics Education......Page 530
Redundancy of Verbal Instructions in Origami Diagrams......Page 538
Origami, Isometries, and Multilayer Tangram......Page 546
Contributors......Page 560