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Geometric Folding Algorithms Linkages, Origami, Polyhedra

ISBN-10: 0521857570

ISBN-13: 9780521857574

Edition: 2007

Authors: Erik D. Demaine, Joseph O'Rourke

List price: $180.00
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Description:

Folding and unfolding problems have been implicit since Albrecht Drer in the early 1500s but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this comprehensive treatment of the geometry of folding and unfolding presents hundreds of results and more than 60 unsolved 'open problems' to spur further research. The authors cover one-dimensional objects (linkages), 2D objects (paper) and 3D objects (polyhedra). Among the results in Part I is that there is a planar linkage that can trace out any algebraic curve, even 'sign your name'. Part II features the 'fold and cut' algorithm, establishing that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut. In Part III readers will see that the 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra. Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers.
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Book details

List price: $180.00
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 7/16/2007
Binding: Hardcover
Pages: 488
Size: 7.50" wide x 10.25" long x 1.00" tall
Weight: 3.036
Language: English

Introduction
Linkages
Problem classification and examples
Upper and lower bounds
Planar linkage mechanisms
Rigid frameworks
Reconfiguration of chains
Locked chains
Interlocked chains
Joint-constrained motion
Protein folding
Introduction
One-dimensional paper
Two-dimensional paper and continuous foldability
Single-vertex foldability
Multi-vertex flat foldability
2D Map folding
Silhouettes and gift wrapping
Tree method
One complete straight cut
Flattening polyhedra
Geometric constructibility
Curved and curved-fold origami
Polyhedra
Introduction and overview
Edge unfolding of polyhedra
Reconstruction of polyhedra
Shortest paths and geodesics
Folding polygons to polyhedra
Higher dimensions.