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Geometric Folding Algorithms

2007-07-16 Computers
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Release : 2007-07-16
Genre : Computers
Kind : eBook
Book Rating : 090/5 ( reviews)

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Book Synopsis Geometric Folding Algorithms by : Erik D. Demaine

Download or read book Geometric Folding Algorithms written by Erik D. Demaine. This book was released on 2007-07-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Folding Algorithms

2014-02-20
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Release : 2014-02-20
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Kind : eBook
Book Rating : 665/5 ( reviews)

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Book Synopsis Geometric Folding Algorithms by : Erik D. Demaine

Download or read book Geometric Folding Algorithms written by Erik D. Demaine. This book was released on 2014-02-20. Available in PDF, EPUB and Kindle. Book excerpt: Lavishly illustrated and entertaining account of the surprising and useful results of the maths of folding and unfolding.

Geometric Folding Algorithms

2008-08-21 Computers
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Release : 2008-08-21
Genre : Computers
Kind : eBook
Book Rating : 225/5 ( reviews)

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Book Synopsis Geometric Folding Algorithms by : Erik D. Demaine

Download or read book Geometric Folding Algorithms written by Erik D. Demaine. This book was released on 2008-08-21. Available in PDF, EPUB and Kindle. Book excerpt: 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 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. 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.

Introduction to Computational Origami

2020-06-29 Computers
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Release : 2020-06-29
Genre : Computers
Kind : eBook
Book Rating : 700/5 ( reviews)

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Book Synopsis Introduction to Computational Origami by : Ryuhei Uehara

Download or read book Introduction to Computational Origami written by Ryuhei Uehara. This book was released on 2020-06-29. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on origami from the point of view of computer science. Ranging from basic theorems to the latest research results, the book introduces the considerably new and fertile research field of computational origami as computer science. Part I introduces basic knowledge of the geometry of development, also called a net, of a solid. Part II further details the topic of nets. In the science of nets, there are numerous unresolved issues, and mathematical characterization and the development of efficient algorithms by computer are closely connected with each other. Part III discusses folding models and their computational complexity. When a folding model is fixed, to find efficient ways of folding is to propose efficient algorithms. If this is difficult, it is intractable in terms of computational complexity. This is, precisely, an area for computer science research. Part IV presents some of the latest research topics as advanced problems. Commentaries on all exercises included in the last chapter. The contents are organized in a self-contained way, and no previous knowledge is required. This book is suitable for undergraduate, graduate, and even high school students, as well as researchers and engineers interested in origami.

Discrete and Computational Geometry

2011-04-11 Mathematics
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Release : 2011-04-11
Genre : Mathematics
Kind : eBook
Book Rating : 983/5 ( reviews)

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Book Synopsis Discrete and Computational Geometry by : Satyan L. Devadoss

Download or read book Discrete and Computational Geometry written by Satyan L. Devadoss. This book was released on 2011-04-11. Available in PDF, EPUB and Kindle. Book excerpt: An essential introduction to discrete and computational geometry Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only)

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