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Geometric Folding Algorithms
Linkages, Origami, Polyhedra

£50.99

  • Date Published: August 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521715225
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About the Authors
  • 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.

    • Fascinating, tangible, accessible cutting-edge research with applications throughout science and engineering
    • Full color throughout
    • Top notch authors: Erik Demaine won a MacArthur fellowship in 2003 for his work on the mathematics of origami
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    Reviews & endorsements

    '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

    'This book is one of those rare mathematics books that I had a hard time putting down. I wanted to keep reading to find the next insight. … This is a serious mathematics book whose explorations have significant applications and real mathematical profundity, wonderfully mixed with some fun recreational mathematics. … The book has a useful index and an extensive bibliography, so when you finish reading, it will remain a valuable resource far into the future. There is a lot of material in this book and it is really a lot of fun. I highly, highly recommend this book to anyone with even a passing interest in folding mathematics.' MAA Reviews

    '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

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    Customer reviews

    23rd Jan 2019 by LauraJason1

    I was attracted by the title Geometric Folding Algorithms: Linkages, Origami, Polyhedra and than more specific on the nameOrigami:! On the moment I'm busy to prepare some Origami related post for my website https://article-writer.net/origami/ and last week I have read the bio form the authors Erik D. Demaine and Joseph O'Rourke. All very interesting!

    Review was not posted due to profanity

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    Product details

    • Date Published: August 2008
    • format: Paperback
    • isbn: 9780521715225
    • length: 496 pages
    • dimensions: 251 x 175 x 25 mm
    • weight: 1.18kg
    • contains: 330 colour illus. 16 tables
    • availability: Available
  • Table of Contents

    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.

  • Authors

    Erik D. Demaine, Massachusetts Institute of Technology
    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.

    Joseph O'Rourke, Smith College, Massachusetts
    Joseph O'Rourke is the Olin Professor of Computer Science at Smith College and the Chair of the Computer Science Department. He recently completed a one-year appointment as Interim Director of Engineering. He has received several grants and awards, including a Presidential Young Investigator Award, a Guggenheim Fellowship, and the NSF Director's Award for Distinguished Teaching Scholars. His research is in the field of computational geometry, where he has published a monograph and a textbook, and he coedited the 1500-page Handbook of Discrete and Computational Geometry. Thirty-one of his more than one hundred papers published in journals and conference proceedings are coauthored with undergraduates.

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