Geometric Folding Algorithms

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Geometric Folding Algorithms

Erik D. Demaine,Joseph O'Rourke
Geometric Folding Algorithms Book PDF

Author : Erik D. Demaine,Joseph O'Rourke
Publisher : Cambridge University Press
Page : 128 pages
File Size : 46,9 Mb
Release : 2007-07-16
Category : Computers
ISBN : 9781107394094

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Geometric Folding Algorithms by Erik D. Demaine,Joseph O'Rourke Pdf

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

Erik D. Demaine,Joseph O'Rourke
Geometric Folding Algorithms Book PDF

Author : Erik D. Demaine,Joseph O'Rourke
Publisher : Cambridge University Press
Page : 496 pages
File Size : 49,9 Mb
Release : 2008-08-21
Category : Computers
ISBN : 0521715229

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Geometric Folding Algorithms by Erik D. Demaine,Joseph O'Rourke Pdf

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

Ryuhei Uehara
Introduction to Computational Origami Book PDF

Author : Ryuhei Uehara
Publisher : Springer Nature
Page : 227 pages
File Size : 40,6 Mb
Release : 2020-06-29
Category : Computers
ISBN : 9789811544705

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Introduction to Computational Origami by Ryuhei Uehara Pdf

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.

Games, Puzzles, and Computation

Robert A. Hearn,Erik D. Demaine
Games Puzzles and Computation Book PDF

Author : Robert A. Hearn,Erik D. Demaine
Publisher : CRC Press
Page : 250 pages
File Size : 40,7 Mb
Release : 2009-06-30
Category : Mathematics
ISBN : 9781439865057

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Games, Puzzles, and Computation by Robert A. Hearn,Erik D. Demaine Pdf

The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computation-quite different from the usual models of automata and circuits-offering a new way of thinking about computation. The appen

Discrete and Computational Geometry

Satyan L. Devadoss,Joseph O'Rourke
Discrete and Computational Geometry Book PDF

Author : Satyan L. Devadoss,Joseph O'Rourke
Publisher : Princeton University Press
Page : 270 pages
File Size : 54,5 Mb
Release : 2011-04-11
Category : Mathematics
ISBN : 9781400838981

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Discrete and Computational Geometry by Satyan L. Devadoss,Joseph O'Rourke Pdf

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).

How to Fold it

Joseph O'Rourke
How to Fold it Book PDF

Author : Joseph O'Rourke
Publisher : Unknown
Page : 177 pages
File Size : 43,8 Mb
Release : 2011
Category : Electronic books
ISBN : 1139234862

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How to Fold it by Joseph O'Rourke Pdf

"What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out"--Provided by publisher.

Origametry

Thomas C. Hull
Origametry Book PDF

Author : Thomas C. Hull
Publisher : Cambridge University Press
Page : 343 pages
File Size : 43,5 Mb
Release : 2020-10-08
Category : Art
ISBN : 9781108478724

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Origametry by Thomas C. Hull Pdf

Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It is an essential reference for researchers of origami mathematics and applications in physics, engineering, and design. Educators, students, and enthusiasts will also enjoy this fascinating account of the mathematics of folding.

Project Origami

Thomas Hull
Project Origami Book PDF

Author : Thomas Hull
Publisher : CRC Press
Page : 365 pages
File Size : 50,6 Mb
Release : 2012-12-21
Category : Mathematics
ISBN : 9781466567917

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Project Origami by Thomas Hull Pdf

Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number theory, and combinatorics. With over 100 new pages, this updated and expanded edition now includes 30 activities and offers better solutions and teaching tips for all activities. The book contains detailed plans for 30 hands-on, scalable origami activities. Each activity lists courses in which the activity might fit, includes handouts for classroom use, and provides notes for instructors on solutions, how the handouts can be used, and other pedagogical suggestions. The handouts are also available on the book’s CRC Press web page. Reflecting feedback from teachers and students who have used the book, this classroom-tested text provides an easy and entertaining way for teachers to incorporate origami into a range of college and advanced high school math courses. Visit the author’s website for more information.

How to Fold It

Joseph O’Rourke
How to Fold It Book PDF

Author : Joseph O’Rourke
Publisher : Cambridge University Press
Page : 191 pages
File Size : 50,6 Mb
Release : 2011-04-25
Category : Mathematics
ISBN : 9781139498548

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How to Fold It by Joseph O’Rourke Pdf

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.

Tribute to a Mathemagician

Barry Cipra,Erik D. Demaine,Martin L. Demaine,Tom Rodgers
Tribute to a Mathemagician Book PDF

Author : Barry Cipra,Erik D. Demaine,Martin L. Demaine,Tom Rodgers
Publisher : CRC Press
Page : 308 pages
File Size : 43,5 Mb
Release : 2004-11-10
Category : Mathematics
ISBN : 9781439864791

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Tribute to a Mathemagician by Barry Cipra,Erik D. Demaine,Martin L. Demaine,Tom Rodgers Pdf

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who's Who in the World of Puzzles---trace their inspiration to Martin Gardner's puzzle column in Scientifi

A History of Folding in Mathematics

Michael Friedman
A History of Folding in Mathematics Book PDF

Author : Michael Friedman
Publisher : Birkhäuser
Page : 419 pages
File Size : 50,9 Mb
Release : 2018-05-25
Category : Mathematics
ISBN : 9783319724874

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A History of Folding in Mathematics by Michael Friedman Pdf

While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.

Geometric Approximation Algorithms

Sariel Har-Peled
Geometric Approximation Algorithms Book PDF

Author : Sariel Har-Peled
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 55,9 Mb
Release : 2011
Category : Approximation algorithms
ISBN : 9780821849118

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Geometric Approximation Algorithms by Sariel Har-Peled Pdf

Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

3-D Geometric Origami

Rona Gurkewitz,Bennett Arnstein
3 D Geometric Origami Book PDF

Author : Rona Gurkewitz,Bennett Arnstein
Publisher : Courier Corporation
Page : 79 pages
File Size : 51,9 Mb
Release : 2012-07-16
Category : Crafts & Hobbies
ISBN : 9780486135601

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3-D Geometric Origami by Rona Gurkewitz,Bennett Arnstein Pdf

Innovative, challenging book provides instructions, diagrams for creating polyhedra models — from the relatively simple tetrahedron to the mind-boggling truncated hexadecahedron.

Twists, Tilings, and Tessellations

Robert J. Lang
Twists Tilings and Tessellations Book PDF

Author : Robert J. Lang
Publisher : CRC Press
Page : 603 pages
File Size : 46,7 Mb
Release : 2017-12-22
Category : Mathematics
ISBN : 9781482262414

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Twists, Tilings, and Tessellations by Robert J. Lang Pdf

Twists, Tilings, and Tessellation describes the underlying principles and mathematics of the broad and exciting field of abstract and mathematical origami, most notably the field of origami tessellations. It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding field.

Computational Geometry

Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong
Computational Geometry Book PDF

Author : Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 50,9 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9783662042458

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Computational Geometry by Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong Pdf

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.