Erik D. Demaine: Geometric Folding Algorithms

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Cover: 9780521857574 | Geometric Folding Algorithms | Linkages, Origami, Polyhedra | Buch

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Sprache: Englisch

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Beschreibung

Folding and unfolding problems have been implicit since Albrecht Dürer 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 over 60 unsolved 'open problems' to spur further research. The authors cover one-dimensional objects (linkages), 2D objects (paper), and 3D objects (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.

Über den Autor

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.

Zusammenfassung

How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results in this comprehensive look at the mathematics of folding. There’s a proof that it’s 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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2014
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	488
Inhalt:	Gebunden
ISBN-13:	9780521857574
ISBN-10:	0521857570
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Demaine, Erik D. O'Rourke, Joseph
Hersteller:	Cambridge University Press
Maße:	260 x 183 x 31 mm
Von/Mit:	Erik D. Demaine (u. a.)
Erscheinungsdatum:	19.02.2014
Gewicht:	1,106 kg

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