Atjaunināt sīkdatņu piekrišanu

E-grāmata: Geometric Folding Algorithms: Linkages, Origami, Polyhedra

4.31/5 (30 ratings by Goodreads)
(Smith College, Massachusetts), (Massachusetts Institute of Technology)
  • Formāts: PDF+DRM
  • Izdošanas datums: 16-Jul-2007
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781139239349
Citas grāmatas par šo tēmu:
  • Formāts - PDF+DRM
  • Cena: 65,42 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
  • Šī e-grāmata paredzēta tikai personīgai lietošanai. E-grāmatas nav iespējams atgriezt un nauda par iegādātajām e-grāmatām netiek atmaksāta.
  • Formāts: PDF+DRM
  • Izdošanas datums: 16-Jul-2007
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781139239349
Citas grāmatas par šo tēmu:

DRM restrictions

  • Kopēšana (kopēt/ievietot):

    nav atļauts

  • Drukāšana:

    nav atļauts

  • Lietošana:

    Digitālo tiesību pārvaldība (Digital Rights Management (DRM))
    Izdevējs ir piegādājis šo grāmatu šifrētā veidā, kas nozīmē, ka jums ir jāinstalē bezmaksas programmatūra, lai to atbloķētu un lasītu. Lai lasītu šo e-grāmatu, jums ir jāizveido Adobe ID. Vairāk informācijas šeit. E-grāmatu var lasīt un lejupielādēt līdz 6 ierīcēm (vienam lietotājam ar vienu un to pašu Adobe ID).

    Nepieciešamā programmatūra
    Lai lasītu šo e-grāmatu mobilajā ierīcē (tālrunī vai planšetdatorā), jums būs jāinstalē šī bezmaksas lietotne: PocketBook Reader (iOS / Android)

    Lai lejupielādētu un lasītu šo e-grāmatu datorā vai Mac datorā, jums ir nepieciešamid Adobe Digital Editions (šī ir bezmaksas lietotne, kas īpaši izstrādāta e-grāmatām. Tā nav tas pats, kas Adobe Reader, kas, iespējams, jau ir jūsu datorā.)

    Jūs nevarat lasīt šo e-grāmatu, izmantojot Amazon Kindle.

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.

Recenzijas

'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

Papildus informācija

Lavishly illustrated and entertaining account of the surprising and useful results of the maths of folding and unfolding.
Preface xi
Introduction
1(8)
Design Problems
1(2)
Foldability Questions
3(6)
Part I. Linkages
Problem Classification and Examples
9(8)
Classification
10(1)
Applications
11(6)
Upper and Lower Bounds
17(12)
General Algorithms and Upper Bounds
17(5)
Lower Bounds
22(7)
Planar Linkage Mechanisms
29(14)
Straight-Line Linkages
29(2)
Kempe's Universality Theorem
31(9)
Hart's Inversor
40(3)
Rigid Frameworks
43(16)
Brief History
43(1)
Rigidity
43(1)
Generic Rigidity
44(5)
Infinitesimal Rigidity
49(4)
Tensegrities
53(4)
Polyhedral Liftings
57(2)
Reconfiguration of Chains
59(27)
Reconfiguration Permitting Intersection
59(8)
Reconfiguration in Confined Regions
67(3)
Reconfiguration Without Self-Crossing
70(16)
Locked Chains
86(37)
Introduction
86(1)
History
87(1)
Locked Chains in 3D
88(4)
No Locked Chains in 4D
92(2)
Locked Trees in 2D
94(2)
No Locked Chains in 2D
96(9)
Algorithms for Unlocking 2D Chains
105(8)
Infinitesimally Locked Linkages in 2D
113(6)
3D Polygons with a Simple Projection
119(4)
Interlocked Chains
123(8)
2-Chains
125(1)
3-Chains
126(1)
4-Chains
127(4)
Joint-Constrained Motion
131(17)
Fixed-Angle Linkages
131(12)
Convex Chains
143(5)
Protein Folding
148(19)
Producible Polygonal Protein Chains
148(6)
Probabilistic Roadmaps
154(4)
HP Model
158(9)
Part II. Paper
Introduction
167(5)
History of Origami
167(1)
History of Origami Mathematics
168(1)
Terminology
169(1)
Overview
170(2)
Foundations
172(21)
Definitions: Getting Started
172(3)
Definitions: Folded States of 1D Paper
175(7)
Definitions: Folding Motions of 1D Paper
182(1)
Definitions: Folded States of 2D Paper
183(4)
Definitions: Folding Motions of 2D Paper
187(2)
Folding Motions Exist
189(4)
Simple Crease Patterns
193(21)
One-Dimensional Flat Foldings
193(5)
Single-Vertex Crease Patterns
198(14)
Continuous Single-Vertex Foldability
212(2)
General Crease Patterns
214(10)
Local Flat Foldability is Easy
214(3)
Global Flat Foldability is Hard
217(7)
Map Folding
224(8)
Simple Folds
225(2)
Rectangular Maps: Reduction to 1D
227(1)
Hardness of Folding Orthogonal Polygons
228(2)
Open Problems
230(2)
Silhouettes and Gift Wrapping
232(8)
Strip Folding
233(1)
Hamiltonian Triangulation
233(3)
Seam Placement
236(1)
Efficient Foldings
237(3)
The Tree Method
240(14)
Origami Bases
240(2)
Uniaxial Bases
242(1)
Everything is Possible
243(1)
Active Paths
244(2)
Scale Optimization
246(1)
Convex Decomposition
247(2)
Overview of Folding
249(1)
Universal Molecule
250(4)
One Complete Straight Cut
254(25)
Straight-Skeleton Method
256(7)
Disk-Packing Method
263(16)
Flattening Polyhedra
279(6)
Connection to Part III: Models of Folding
279(1)
Connection to Fold-and-Cut Problem
280(1)
Solution via Disk Packing
281(1)
Partial Solution via Straight Skeleton
281(4)
Geometric Constructibility
285(7)
Trisection
285(1)
Huzita's Axioms and Hatori's Addition
285(3)
Constructible Numbers
288(1)
Folding Regular Polygons
289(1)
Generalizing the Axioms to Solve All Polynomials?
290(2)
Rigid Origami and Curved Creases
292(7)
Folding Paper Bags
292(1)
Curved Surface Approximation
293(3)
David Huffman's Curved-Folds Origami
296(3)
Part III. Polyhedra
Introduction and Overview
299(7)
Overview
299(2)
Curvature
301(3)
Gauss-Bonnet Theorem
304(2)
Edge Unfolding of Polyhedra
306(33)
Introduction
306(6)
Evidence for Edge Unfoldings
312(1)
Evidence against Edge Unfoldings
313(5)
Unfoldable Polyhedra
318(3)
Special Classes of Edge-Unfoldable Polyhedra
321(12)
Vertex Unfoldings
333(6)
Reconstruction of Polyhedra
339(19)
Cauchy's Rigidity Theorem
341(4)
Flexible Polyhedra
345(3)
Alexandrov's Theorem
348(6)
Sabitov's Algorithm
354(4)
Shortest Paths and Geodesics
358(23)
Introduction
358(4)
Shortest Paths Algorithms
362(4)
Star Unfolding
366(6)
Geodesics: Lyusternik--Schnirelmann
372(3)
Curve Development
375(6)
Folding Polygons to Polyhedra
381(56)
Folding Polygons: Preliminaries
381(5)
Edge-to-Edge Gluings
386(6)
Gluing Trees
392(4)
Exponential Number of Gluing Trees
396(3)
General Gluing Algorithm
399(3)
The Foldings of the Latin Cross
402(9)
The Foldings of a Square to Convex Polyhedra
411(7)
Consequences and Conjectures
418(8)
Enumerations of Foldings
426(3)
Enumerations of Cuttings
429(2)
Orthogonal Polyhedra
431(6)
Higher Dimensions
437(6)
Part I
437(1)
Part II
437(1)
Part III
438(5)
Bibliography 443(18)
Index 461


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 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.