Origami 3 Third International Meeting of Origami Science, Mathematics, and Education

Contents......Page 5
Preface......Page 9
Part One: Mathematics of Origami......Page 12
Recent Results in Computational Origami......Page 14
A Disk-Packing Algorithm for an Origami Magic Trick......Page 28
The Combinatorics of Flat Folds: A Survey......Page 40
A Mathematical Model for Non-Flat Origami......Page 50
The Definition of Iso-Area Folding......Page 63
The Geometry of Orizuru......Page 70
The Validity of the Orb, an Origami Model......Page 83
Mathematical Origami: Another View of Alhazen's Optical Problem......Page 91
Just Like Young Gauss Playing with a Square: Folding the Regular 17-gon......Page 102
Paper-Folding Constructions in Euclidean Geometry: An Exercise in Thrift......Page 114
Part Two: Origami Science and Applications......Page 125
Computer Tools and Algorithms for Origami Tessellation Design......Page 127
The Foldinator Modeler and Document Generator......Page 134
The Application of Origami Science to Map and Atlas Design......Page 141
Origami Pots Tomoko Fuse, Akira Nagashima, Yasuhiro Ohara......Page 150
Polypolyhedra in Origami......Page 156
Origami with Trigonometric Functions......Page 171
A Study of Twist Boxes......Page 181
To Fold or to Crumple?......Page 189
Folded Tubes as Compared to Kikko ("Tortoise-Shell") Bamboo......Page 198
Square Cycles: An Introduction to the Analysis of Flexagons......Page 209
Self-Assembling Global Shape Using Concepts from Origami......Page 218
Part Three: Origami in Education......Page 231
Applications of Origami to the Teaching of Sophisticated Communication Techniques......Page 233
Origami and the Adult ESL Learner......Page 245
Exploring the Possibilities of a Module......Page 255
Using Graphs to Color Origami Polyhedra......Page 266
Circular Origami: A Survey of Recent Results......Page 280
In Praise of the Papercup: Mathematics and Origami at the University......Page 288
Using Triangular Boxes from Rectangular Paper to Enrich Trigonometry and Calculus......Page 296
Fold Paper and Enjoy Math: Origamics......Page 303
Origami as a Model for Development in Organisms......Page 325
Instances of Origami within Mathematics Content Texts for Preservice Elementary School Teachers......Page 332
Contributors......Page 340