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Connections: The Geometric Bridge Between Art & Science (2nd Edition) 2nd Revised edition [Hardback]

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(New Jersey Inst Of Technology, Usa)
  • Formāts: Hardback, 520 pages
  • Sērija : Series on Knots & Everything 25
  • Izdošanas datums: 29-Nov-2001
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9810245858
  • ISBN-13: 9789810245856
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Connections: The Geometric Bridge Between Art & Science (2nd Edition) 2nd Revised editionPalielināt
  • Formāts: Hardback, 520 pages
  • Sērija : Series on Knots & Everything 25
  • Izdošanas datums: 29-Nov-2001
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9810245858
  • ISBN-13: 9789810245856
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9789810245856.html
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in Mathematics, Chemistry, and Astronomy Professional and Reference in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition.
Preface xi
Acknowledgements xv
Credits xvii
Preface to the Second Edition xxiii
Proportion in Architecture
1(34)
Introduction
1(1)
Myth and Number
2(5)
Proportion and Number
7(2)
The Structure of Ancient Musical Scales
9(3)
The Musical Scale in Architecture
12(4)
Systems of Proportion Based on √2, Θ, and φ
16(5)
The Golden Mean and Its Application to the Modulor of Le Corbusier
21(7)
An Ancient System of Roman Proportion
28(7)
Appendix 1.A
32(3)
Similarity
35(40)
Introduction
35(1)
Similarity
36(1)
Families of Similar Figures
37(1)
Self-Similarity of the Right Triangle
38(3)
Line Choppers
41(1)
A Circle Chopper
41(2)
Construction of the Square Root of a Given Length
43(1)
Archimedes Spiral
43(2)
Logarithmic Spiral
45(3)
Growth and Similarity in Nature
48(4)
Growth and Similarity in Geometry
52(3)
Infinite Self-Similar Curves
55(8)
On Growth and Form
63(12)
Appendix 2.A
65(2)
Appendix 2.B
67(8)
The Golden Mean
75(30)
Introduction
75(1)
Fibonacci Series
76(5)
Some Tiling Properties of φ
81(1)
The Golden Rectangle and the Golden Section
82(3)
The Golden Mean Triangle
85(1)
The Pentagon and Decagon
86(3)
The Golden Mean and Patterns of Plant Growth
89(8)
The Music of Bartok: A System Both Open and Closed
97(8)
Graphs
105(62)
Introduction
105(1)
Graphs
105(9)
Maps
114(3)
Maps and Graphs on a Sphere
117(2)
Connectivity of Graphs and Maps
119(1)
Combinatorial Properties
120(2)
Regular Maps
122(2)
New Graphs from Old Ones
124(1)
Duality
125(2)
Planar and Nonplanar Graphs
127(2)
Maps and Graphs on Other Surfaces
129(5)
The Torus and the Moblus Strip
134(3)
Magic Squares
137(1)
Map Coloring
138(3)
Regular Maps on a Torus
141(1)
Szilassi and Csaszar Maps
142(3)
Floor Plans
145(9)
8racing Structures
154(5)
Eulerian Paths
159(4)
Hamiltonian Paths
163(4)
Tilings with Polygons
167(42)
Introduction
167(2)
Polygons
169(4)
Regular Tilings of the Plane
173(4)
Duality
177(1)
Semiregular Tilings
177(1)
Symmetry
178(3)
Duality of Semiregular Tilings
181(1)
The Module of a Semiregular Tiling
182(1)
Other Tilings with Regular Polygons
183(1)
Transformations of Regular Tiling
183(11)
Nonperiodic Tilings
194(4)
Origami Patterns
198(2)
Islamic Art
200(9)
Two-Dimensional Networks and Lattices
209(46)
Introduction
209(1)
Planar Soap Films
209(5)
Random Cellular Networks
214(3)
Rural Market Networks
217(3)
Dirichlet Domains
220(4)
Spider Webs, Dirichlet Domains, and Rigidity
224(6)
Lattices
230(4)
Pattern Generation with Lattices
234(4)
Dirichlet Domains of Lattices and Their Relation to Plant Growth
238(5)
Quasicrystals and Penrose Tiles
243(12)
Appendix 6.A Projective Geometry
248(7)
Polyhedra: Platonic Solids
255(40)
Introduction
255(2)
The Platonic Solids
257(2)
The Platonic Solids as Regular Polyhedra
259(2)
Maps of Regular Polyhedra on a Circumscribed Sphere
261(2)
Maps of the Regular Polyhedra on the Plane-Schlegel Diagrams
263(1)
Duality
264(4)
Combinatorial Properties
268(2)
Rigidity
270(3)
The Angular Deficit
273(2)
From Maps to Polyhedra-The Dihedral Angle
275(2)
Space-Filling Properties
277(2)
Juxtapositions
279(3)
Symmetry
282(6)
Star Polyhedra
288(7)
Appendix 7.A Duals
291(1)
Appendix 7.B A Proof of Descartes Formula
292(3)
Appendix 7.C
Transformation of the Platonic Solids I
295(32)
Introduction
295(1)
Intermediate Polyhedra
296(3)
Interpenetrating Duals Revisited
299(2)
The Rhombic Dodecahedron
301(2)
Embeddings Based on Symmetry
303(3)
Designs Based on Symmetry Breaking
306(2)
Relation to the Golden Mean
308(2)
Tensegrities
310(3)
The Tetrahedron--Methane Molecule Molecule and Soap Bubble
313(2)
Tetrahedron as the Atom of Structure
315(2)
Packing of Spheres
317(6)
Geodesic Domes and Viruses
323(4)
Transformation of the Platonic Solids II
327(20)
Introduction
327(1)
Archimedean Solids
327(2)
Truncation
329(3)
The Truncated Octahedron
332(2)
The Snub Figures
334(1)
Archimedean Duals
335(1)
Maps on a Sphere
335(2)
Combinatorial Properties
337(2)
Symmetry Revisited
339(2)
Prisms and Antiprisms
341(6)
Polyhedra: Space Filling
347(36)
Introduction
347(1)
Close Packing of Spheres
347(3)
The Shape of Space
350(3)
Packing Ratios
353(2)
Three-Dimensional Lattices
355(1)
Dirichlet Domains
356(1)
Crystal Structure
357(3)
Networks
360(2)
Infinite Regular Surfaces
362(3)
The Diamond and Graphite Nets
365(3)
Soap Froths
368(1)
A Unified Look at Nets Related to Cubic Lattices
369(2)
Zonohedra
371(6)
Golden Isozonohedra
377(6)
Isometries and Mirrors
383(22)
Introduction
383(1)
Mirrors
384(2)
Sets
386(1)
Mappings
387(3)
Translations
390(1)
Rotations
391(1)
Reflections
392(1)
Glide Reflection
393(1)
Proper and Improper Transformations
394(1)
Isometries and Mirrors
395(7)
Some Reflection Exercises
402(1)
Some Additional Relations Involving Isometries
403(2)
Symmetry of the Plane
405(48)
Introduction
405(3)
The Mathematics of Symmetry
408(2)
Symmetry Groups
410(1)
Subsets of a Group
411(2)
Kaleidoscope Groups
413(2)
Pattern Generation and the Kaleidoscope
415(2)
A Colored Kaleidoscope Symmetry
417(2)
Some Other Examples of Pattern Generation
419(1)
Pattern Generation in Hyperbolic Geometry
420(2)
Line Symmetry
422(3)
The Two-Dimensional Ornamental Symmetry Groups
425(5)
Symmetry and Design
430(2)
A Fundamental Postulate
432(3)
Interaction of Two Rotocenters Implies a Third
435(2)
Nets
437(1)
Enantiomorphy
438(5)
Aesthetics of Wallpaper Patterns
443(2)
The Symmetry of Islamic Tilings
445(1)
Symmetry of Similarity
446(7)
Epilogue 453(2)
References 455(8)
Index 463(10)
Supplements 473(14)
New References for the Second Edition 487