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

Contents......Page 4
Preface......Page 8
I. Origami in Design and Art......Page 11
Paper Nautili: A Model for Three-Dimensional Planispiral Growth......Page 12
Curves and Flats......Page 18
The Celes Family of Modular Origami......Page 30
Fractal Crease Patterns......Page 40
Constructing Regular n-gonal Twist Boxes......Page 50
A Brief History of Oribotics......Page 59
Graphics Transformation of Origami Models......Page 69
One-Dimensional Origami: Polyhedral Skeletons in Dance......Page 83
II. Origami and Technology......Page 92
The Science of Miura-Ori: A Review......Page 93
Origami-Inspired Self-Assembly......Page 106
Expandable Tubes with Negative Poisson’s Ratio and Their Application in Medicine......Page 122
Airbag Folding Based on Origami Mathematics......Page 133
III. Computational Origami......Page 144
Surface Transitions in Curved Origami......Page 145
Folding Curves......Page 153
The Method for Judging Rigid Foldability......Page 166
Simulation of Rigid Origami......Page 176
Facet Ordering and Crease Assignment in Uniaxial Bases......Page 189
Integer Programming Models for Flat Origami......Page 206
Construction of 3D Virtual Origami Models from Sketches......Page 216
An Excel-Based Solution to the One-Cut Folding Problem......Page 228
Computer Origami Simulation and the Production of Origami Instructions......Page 236
Recognition, Modeling, and Rendering Method for Origami Using 2D Bar Codes......Page 249
3D Origami Design Based on Tucking Molecules......Page 257
eGami: Virtual Paperfolding and Diagramming Software......Page 271
Computational Origami System Eos......Page 282
Computational Complexity of a Pop-Up Book......Page 291
Concepts and Modeling of a Tessellated Molecule Surface......Page 301
Folding Paper Shopping Bags......Page 311
Origamic Architecture in the Cartesian Coordinate System......Page 330
IV. Origami Mathematics......Page 343
How Many Ways Can You Edge-Color a Cube?......Page 344
Configuration Spaces for Flat Vertex Folds......Page 354
One-, Two-, and Multi-Fold Origami Axioms......Page 364
The Power of Multifolds: Folding the Algebraic Closure of the Rational Numbers......Page 387
Fujimoto, Number Theory, and a New Folding Technique......Page 397
On the Fish Base Crease Pattern and Its Flat Foldable Property......Page 408
Orizuru Deformation Theory for Unbounded Quadrilaterals......Page 418
A Crystal Map of the Orizuru World......Page 430
A Geometrical Tree of Fortune Cookies......Page 440
V. Origami in Education......Page 448
Origametria: A Program to Teach Geometry and to Develop Learning Skills Using the Art of Origami......Page 449
The Impact of Origami-Mathematics Lessons on Achievement and Spatial Ability of Middle-School Students......Page 460
Understanding the Effect of Origami Practice, Cognition, and Language on Spatial Reasoning......Page 471
Modular Origami in the Secondary Geometry Classroom......Page 484
On the Effective Use of Origami in the Mathematics Classroom......Page 493
Using Origami to Promote Problem Solving, Creativity, and Communication in Mathematics Education......Page 502
Redundancy of Verbal Instructions in Origami Diagrams......Page 510
Origami, Isometries, and Multilayer Tangram......Page 518
Contributors......Page 531