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

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. 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 "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."--Jacket Contains select contributions from the Fourth International Conference on Origami in Science, Mathematics, and Education (4OSME), held September 8-10, 2006, in Pasadena, CA. The conference has been held approximately once every five years, and it focuses on the mathematics of origami and applications of origami in the sciences.