Geometric Folding Algorithms

Linkages, Origami, Polyhedra

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Hardcover | 16 July 2007

At a Glance

Hardcover
488 Pages

Dimensions(cm)
25.4 x 17.78 x 2.69

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How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results and over 60 unsolved 'open problems' in this comprehensive look at the mathematics of folding, with an emphasis on algorithmic or computational aspects. Folding and unfolding problems have been implicit since Albrecht Durer 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. A proof shows that it is possible to design a series of jointed bars moving only in a flat plane that can sign a name or trace any other algebraic curve. One remarkable algorithm shows you can fold any straight-line drawing on paper so that the complete drawing can be cut out with one straight scissors cut. 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.

Industry Reviews

'Demaine and O'Rourke are among the best-qualified authors for a book on this subject; and the book that they have written is a delight ... it is exceptionally clear and readable. It could be read for pleasure by any mathematics undergraduate, and much of it (though not all) by amateurs with a high school mathematics background ... although there are sections that some amateurs will skip, the level is always kept as elementary as locally possible. This book should be in all university libraries, and many professional and amateur mathematicians will want to add it to their personal collections.' Robert Dawson (Halifax), Zentralblatt Math

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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.
Table of Contents provided by Publisher. All Rights Reserved.

Geometric Folding Algorithms

Linkages, Origami, Polyhedra

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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Arithmetic Quotients of the Bruhat-Tits Building for Projective GeneralLinear Groups in Positive Characteristic

The Global Solutions to a Cartan's Realization Problem

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Finite and Infinite Dimension

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