Geometric Folding Algorithms

Geometric Folding Algorithms

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.

Author: Erik D. Demaine

Publisher: Cambridge University Press

ISBN: 9781107394094

Category: Computers

Page:

View: 317

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.
Categories: Computers

How to Fold It

How to Fold It

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.

Author: Joseph O’Rourke

Publisher: Cambridge University Press

ISBN: 9781139498548

Category: Mathematics

Page:

View: 579

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.
Categories: Mathematics

3D Origami Art

3D Origami Art

... closely related to geometry. Origami research has been conducted in the field of mathematics since olden times. ... The book by Demaine and O'Rourke, Geometric Folding Algorithms: Linkages, Origami, Polyhedra* covers these topics.

Author: Jun Mitani

Publisher: CRC Press

ISBN: 9781315350400

Category: Mathematics

Page: 114

View: 605

Easily Create Origami with Curved Folds and Surfaces Origami—making shapes only through folding—reveals a fascinating area of geometry woven with a variety of representations. The world of origami has progressed dramatically since the advent of computer programs to perform the necessary computations for origami design. 3D Origami Art presents the design methods underlying 3D creations derived from computation. It includes numerous photos and design drawings called crease patterns, which are available for download on the author’s website. Through the book’s clear figures and descriptions, readers can easily create geometric 3D structures out of a set of lines and curves drawn on a 2D plane. The author uses various shapes of sheets such as rectangles and regular polygons, instead of square paper, to create the origami. Many of the origami creations have a 3D structure composed of curved surfaces, and some of them have complicated forms. However, the background theory underlying all the creations is very simple. The author shows how different origami forms are designed from a common theory.
Categories: Mathematics

Algorithms and Computation

Algorithms and Computation

Demaine, E.D., O'Rourke, J.: Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press (2007) 7. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) ...

Author: Takao Asano

Publisher: Springer

ISBN: 9783642255915

Category: Computers

Page: 775

View: 350

This book constitutes the refereed proceedings of the 22nd International Symposium on Algorithms and Computation, ISAAC 2011, held in Yokohama, Japan in December 2011. The 76 revised full papers presented together with two invited talks were carefully reviewed and selected from 187 submissions for inclusion in the book. This volume contains topics such as approximation algorithms; computational geometry; computational biology; computational complexity; data structures; distributed systems; graph algorithms; graph drawing and information visualization; optimization; online and streaming algorithms; parallel and external memory algorithms; parameterized algorithms; game theory and internet algorithms; randomized algorithms; and string algorithms.
Categories: Computers

Project Origami

Project Origami

... Can Origami Trisect an Angle?, and Solving Cubic Equations activities in an advanced algebra class should consult this book. Geometric Folding Algorithms: Linkages, Origami, Polyhedra by Erik Demaine and Joseph O'Rourke [Dem07].

Author: Thomas Hull

Publisher: CRC Press

ISBN: 9781466568099

Category: Mathematics

Page: 364

View: 554

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
Categories: Mathematics

WALCOM Algorithms and Computation

WALCOM  Algorithms and Computation

Among convex polyhedra with regular polygonal faces, including the Platonic solids, the Archimedean solids, and the JZ solids, regular prisms, ... Demaine, E.D., O'Rourke, J.: Geometric Folding Algorithms: Linkages, Origami, Polyhedra.

Author: M. Sohel Rahman

Publisher: Springer

ISBN: 9783319156125

Category: Computers

Page: 336

View: 760

This book constitutes the thoroughly refereed conference proceedings of the 9th International Workshop on Algorithms and Computation, WALCOM 2015, held in Dhaka, Bangladesh, in February 2015. The 26 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 85 submissions. The papers are organized in topical sections on approximation algorithms, data structures and algorithms, computational geometry, combinatorial algorithms, distributed and online algorithms, graph drawing and algorithms, combinatorial problems and complexity, and graph enumeration and algorithms.
Categories: Computers

Handbook of Discrete and Computational Geometry

Handbook of Discrete and Computational Geometry

An energy - driven approach to linkage unfolding . In Proc . ... Infinitesimally locked self - touching linkages with applications to locked trees . ... 6.849 : Geometric folding algorithms : Linkages , origami , polyhedra .

Author: Csaba D. Toth

Publisher: CRC Press

ISBN: 9781498711425

Category: Computers

Page: 1928

View: 600

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Categories: Computers

Computational Geometry Graphs and Applications

Computational Geometry  Graphs and Applications

In: Proceedings of the 16th Canadian Conference on Computational Geometry, Montréal, Canada, pp. 64–67 (August 2004) 6. Demaine, E.D., O'Rourke, J.: Geometric Folding Algorithms: Linkages, Origami, Polyhedra.

Author: Jin Akiyama

Publisher: Springer Science & Business Media

ISBN: 9783642249822

Category: Computers

Page: 227

View: 574

This book constitutes the thoroughly refereed post-conference proceedings of the China-Japan Joint Conference on Computational Geometry, Graphs and Applications, CGGA 2010, held in Dalian, China, in November 2010. The 23 revised full papers presented were carefully selected during two rounds of reviewing and improvement from numerous submissions. All aspects of computational and discrete geometry, graph theory, graph algorithms, and their applications are covered.
Categories: Computers

Introduction to Computational Origami

Introduction to Computational Origami

The World of New Computational Geometry Ryuhei Uehara ... 277–288 [DO07] E.D. Demaine, J. O'Rourke, Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Cambridge, 2007) Chapter 11 Undecidability of Folding Abstract The ...

Author: Ryuhei Uehara

Publisher: Springer Nature

ISBN: 9789811544705

Category: Computers

Page: 220

View: 655

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.
Categories: Computers

On Paper

On Paper

One of his MIT classes, “Geometric Folding Algorithms: Linkages, Origami, Polyhedra,” concerns the reconfiguring of physical objects. At the heart of the course are joint projects intended “to solve open problems in folding,” ...

Author: Nicholas A. Basbanes

Publisher: Vintage

ISBN: 9780385350440

Category: History

Page: 448

View: 794

A Best Book of the Year: Mother Jones • Bloomberg News • National Post • Kirkus In these pages, Nicholas Basbanes—the consummate bibliophile’s bibliophile—shows how paper has been civilization’s constant companion. It preserves our history and gives record to our very finest literary, cultural, and scientific accomplishments. Since its invention in China nearly two millennia ago, the technology of paper has spread throughout the inhabited world. With deep knowledge and care, Basbanes traces paper’s trail from the earliest handmade sheets to the modern-day mills. Paper, yoked to politics, has played a crucial role in the unfolding of landmark events, from the American Revolution to Daniel Ellsberg’s Pentagon Papers to the aftermath of 9/11. Without paper, modern hygienic practice would be unimaginable; as currency, people will do almost anything to possess it; and, as a tool of expression, it is inextricable from human culture. Lavishly researched, compellingly written, this masterful guide illuminates paper’s endless possibilities.
Categories: History