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Geometric Folding Algorithms: Linkages, Origami, Polyhedra 1st edition by Demaine, Erik D., O'Rourke, Joseph (2007) Hardcover

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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.

Hardcover

First published July 16, 2007

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About the author

Erik D. Demaine

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Erik D. Demaine is a professor of Computer Science at the Massachusetts Institute of Technology and a former child prodigy. Demaine's research interests range throughout algorithms, from data structures for improving web searches to the geometry of understanding how proteins fold to the computational difficulty of playing games. He received a MacArthur Fellowship as a “computational geometer tackling and solving difficult problems related to folding and bending—moving readily between the theoretical and the playful, with a keen eye to revealing the former in the latter”. He appears in the recent origami documentary Between the Folds, cowrote a book about the theory of folding (Geometric Folding Algorithms), and a book about the computational complexity of games (Games, Puzzles, and Computation). Together with his father Martin, his interests span the connections between mathematics and art, including curved-crease sculptures in the permanent collections of the Museum of Modern Art in New York, and the Renwick Gallery in the Smithsonian.

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