Origami 3: Third International Meeting of Origami Science, Mathematics, and Education Sponsored by Origami USA

The book contains papers from the proceedings of the 3rd International Meeting of Origami Science, Math, and Education, sponsored by OrigamiUSA. They cover topics ranging from the mathematics of origami using polygon constructions and geometric projections, applications, and science of origami, and the use of origami in 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 The 31 papers do not necessarily pay more attention than other studies to the three-dimensional aspects of the Japanese paper-folding art: the cubed title refers to the number of the conference. They discuss such topics as a disk-packing algorithm for an origami magic trick, polypolyhedra, and origami and the adult learner of English as a second language. Annotation copyrighted by Book News, Inc., Portland, OR By "the mathematics of paper-folding," we mean an attempt to learn the "hows and whys" of paper-folding by modeling the process with mathematics.