Geometric Folding Algorithms

ISBN-13: 9780521715225 / Angielski / Miękka / 2008 / 488 str.

Erik D. Demaine; Joseph O'Rourke

Opis

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.

Recenzje

'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

Spis treści

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.