Erik D. Demaine

Geometric Folding Algorithms (eBook, PDF)

Linkages, Origami, Polyhedra

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 16. Juli 2007
• Englisch
• ISBN-13: 9781139239349
• Artikelnr.: 39959615

Autorenporträt

Erik D. Demaine is the Esther and Harold E. Edgerton Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, where he joined the faculty in 2001. He is the recipient of several awards, including the MacArthur Fellowship, the Harold E. Edgerton Faculty Achievement Award, the Ruth and Joel Spira Award for Distinguished Teaching, and the NSERC Doctoral Prize. His research interests range throughout algorithms from data structures for improving web searches to the geometry of understanding how proteins relate to the computational difficulty of playing games. He has published more than 150 papers with more than 150 collaborators and coedited the book Tribute to a Mathemagician in honor of the influential recreational mathematician Martin Gardner.

Inhaltsangabe

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.