Origametry: Mathematical Methods in Paper FoldingOrigami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding. |
Contents
Introduction page | 1 |
Examples and Basic Folds | 11 |
Solving Equations via Folding | 31 |
Origami Algebra | 48 |
Beyond Classic Origami | 58 |
6 | 107 |
7 | 137 |
8 | 159 |
Folding Manifolds | 191 |
An Analytic Approach to Isometric Foldings | 217 |
Rigid Origami | 231 |
Rigid Foldings | 256 |
Rigid Origami Theory | 290 |
| 319 | |
| 330 | |
9 | 181 |
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Common terms and phrases
allow assume base boundary called Chapter circle closed coloring complex condition cone configuration space connected consider construction contains convex corresponding crease lines crease pattern create cross curve define Definition degree-4 Demaine denote describe determine direction Diversion edges equal Equation example exists faces fact flat flat origami flat vertex fold flat-foldable folding angles force function gadget geometry given gives graph interior intersect isometric folding Kawasaki’s layers Lemma length mathematics matrix means method mode mountain MV assignment Note operation origin paper path plane polygon positive possible problem proof prove region result rigid folding rigid origami rotation satisfy seen sequence shown in Figure shows side single-vertex solve sphere spherical square surface tangent Theorem trace triangle TRUE twist unfolded valid valley values vector vertices wires