Geometric Folding Algorithms
Linkages, Origami, Polyhedra

Lavishly illustrated and entertaining account of the surprising and useful results of the maths of folding and unfolding.

Erik D. Demaine (Author), Joseph O'Rourke (Author)

9780521715225, Cambridge University Press

Paperback, published 21 August 2008

496 pages, 82 b/w illus. 330 colour illus. 16 tables
25.1 x 17.5 x 2.5 cm, 1.18 kg

'The authors explain step-by-step interesting solutions of some folding problems. This splendidly illustrated book can be interesting for advanced undergraduate students in mathematics and computer science as well as for geometers and computer specialists who can find many new ideas and impulses …' EMS Newsletter

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

Introduction
Part I. Linkages: 1. Problem classification and examples
2. Upper and lower bounds
3. Planar linkage mechanisms
4. Rigid frameworks
5. Reconfiguration of chains
6. Locked chains
7. Interlocked chains
8. Joint-constrained motion
9. Protein folding
Part II. Paper: 10. Introduction
11. Foundations
12. Simple crease patterns
13. General crease patterns
14. Map folding
15. Silhouettes and gift wrapping
16. The tree method
17. One complete straight cut
18. Flattening polyhedra
19. Geometric constructibility
20. Rigid origami and curved creases
Part III. Polyhedra: 21. Introduction and overview
22. Edge unfolding of polyhedra
23. Reconstruction of polyhedra
24. Shortest paths and geodesics
25. Folding polygons to polyhedra
26. Higher dimensions.

Subject Areas: Algorithms & data structures [UMB], Geometry [PBM]