Connections The Geometric Bridge Between Art and Science

Name: Connections The Geometric Bridge Between Art and Science
Price: 3.93 USD
Availability: InStock
ISBN: 9780070342507

ISBN-10: 0070342504

ISBN-13: 9780070342507

Edition: 1st 1991

Authors: Jay Kappraff

List price: $40.00

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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…

Book details

List price: $40.00
Edition: 1st
Copyright year: 1991
Publisher: McGraw-Hill Companies, The
Binding: Hardcover
Pages: 471
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 1.584
Language: English

Daoud, CEA-CNRS, Gif-sur-Yvette.The author is an Associate Professor at NJIT since 1974. Professor Jay Kapraff is also the author of the book ? Connections: The Geometric Bridge between Art and Science, which was chosen by the National Association of Publishers (USA) as the best book in ? Mathematics, Chemistry and Astronomy ? Professional and Reference? in 1991. He is selected for Who's Who in Science and Technology in 1983 and Who's Who in American Education in 1993. He has also received the CAPE award from Cable TV of NJ for best Distance Learning Course of 1996.

Preface	p. xi
Acknowledgements	p. xv
Credits	p. xvii
Preface to the Second Edition	p. xxiii
Proportion in Architecture	p. 1
Introduction	p. 1
Myth and Number	p. 2
Proportion and Number	p. 7
The Structure of Ancient Musical Scales	p. 9
The Musical Scale in Architecture	p. 12
Systems of Proportion Based on [radical]2, [theta], and [phi]	p. 16
The Golden Mean and Its Application to the Modulor of Le Corbusier	p. 21
An Ancient System of Roman Proportion	p. 28
Appendix 1.A	p. 32
Similarity	p. 35
Introduction	p. 35
Similarity	p. 36
Families of Similar Figures	p. 37
Self-Similarity of the Right Triangle	p. 38
Line Choppers	p. 41
A Circle Chopper	p. 41
Construction of the Square Root of a Given Length	p. 43
Archimedes Spiral	p. 44
Logarithmic Spiral	p. 45
Groth and Similarity in Nature	p. 48
Growth and Similarity in Geometry	p. 52
Infinite Self-Similar Curves	p. 55
On Growth and Form	p. 63
Appendix 2.A	p. 65
Appendix 2.B	p. 67
The Golden Mean	p. 75
Introduction	p. 75
Fibonacci Series	p. 76
Some Tiling Properties of [phi]	p. 81
The Golden Rectangle and the Golden Section	p. 82
The Golden Mean Triangle	p. 85
The Pentagon and Decagon	p. 86
The Golden Mean and Patterns of Plant Growth	p. 89
The Music of Bartok: A System Both Open and Closed	p. 97
Graphs	p. 105
Introduction	p. 105
Graphs	p. 108
Maps	p. 114
Maps and Graphs on a Sphere	p. 117
Connectivity of Graphs and Maps	p. 119
Combinatorial Properties	p. 120
Regular Maps	p. 122
New Graphs from Old Ones	p. 124
Duality	p. 125
Planar and Nonplanar Graphs	p. 127
Maps and Graphs on Other Surfaces	p. 129
The Torus and the Moblus Strip	p. 134
Magic Squares	p. 137
Map Coloring	p. 138
Regular Maps on a Torus	p. 141
Szilassi and Csaszar Maps	p. 142
Floor Plans	p. 145
Bracing Structures	p. 154
Eulerian Paths	p. 159
Hamiltonian Paths	p. 163
Tilings with Polygons	p. 167
Introduction	p. 167
Polygons	p. 169
Regular Tilings of the Plane	p. 173
Duality	p. 177
Semiregular Tilings	p. 177
Symmetry	p. 178
Duality of Semiregular Tilings	p. 181
The Module of a Semiregular Tiling	p. 182
Other Tilings with Regular Polygons	p. 183
Transformations of Regular Tiling	p. 183
Nonperiodic Tilings	p. 194
Origami Patterns	p. 198
Islamic Art	p. 200
Two-Dimensional Networks and Lattices	p. 209
Introduction	p. 209
Planar Soap Films	p. 209
Random Cellular Networks	p. 214
Rural Market Networks	p. 217
Dirichlet Domains	p. 220
Spider Webs, Dirichlet Domains, and Rigidity	p. 224
Lattices	p. 230
Pattern Generation with Lattices	p. 234
Dirichlet Domains of Lattices and Their Relation to Plant Growth	p. 238
Quasicrystals and Penrose Tiles	p. 243
Projective Geometry	p. 248
Polyhedra: Platonic Solids	p. 255
Introduction	p. 255
The Platonic Solids	p. 257
The Platonic Solids as Regular Polyhedra	p. 259
Maps of Regular Polyhedra on a Circumscribed Sphere	p. 261
Maps of the Regular Polyhedra on the Plane-Schlegel Diagrams	p. 263
Duality	p. 264
Combinatorial Properties	p. 268
Rigidity	p. 270
The Angular Deficit	p. 273
From Maps to Polyhedra-The Dihedral Angle	p. 275
Space-Filling Properties	p. 277
Juxtapositions	p. 279
Symmetry	p. 282
Star Polyhedra	p. 288
Duals	p. 291
A Proof of Descartes Formula	p. 292
Appendix 7.C
Transformation of the Platonic Solids I	p. 295
Introduction	p. 295
Intermediate Polyhedra	p. 296
Interpenetrating Duals Revisited	p. 299
The Rhombic Dodecahedron	p. 301
Embeddings Based on Symmetry	p. 303
Designs Based on Symmetry Breaking	p. 306
Relation to the Golden Mean	p. 308
Tensegrities	p. 310
The Tetrahedron-Methane Molecule Molecule and Soap Bubble	p. 313
Tetrahedron as the Atom of Structure	p. 315
Packing of Spheres	p. 317
Geodesic Domes and Viruses	p. 323
Transformation of the Platonic Solids II	p. 327
Introduction	p. 327
Archimedean Solids	p. 327
Truncation	p. 329
The Truncated Octahedron	p. 332
The Snub Figures	p. 334
Archimedean Duals	p. 335
Maps on a Sphere	p. 335
Combinatorial Properties	p. 337
Symmetry Revisited	p. 339
Prisms and Antiprisms	p. 341
Polyhedra: Space Filling	p. 347
Introduction	p. 347
Close Packing of Spheres	p. 347
The Shape of Space	p. 350
Packing Ratios	p. 353
Three-Dimensional Lattices	p. 355
Dirichlet Domains	p. 356
Crystal Structure	p. 357
Networks	p. 360
Infinite Regular Surfaces	p. 362
The Diamond and Graphite Nets	p. 365
Soap Froths	p. 368
A Unified Look at Nets Related to Cubic Lattices	p. 369
Zonohedra	p. 371
Golden Isozonohedra	p. 377
Isometries and Mirrors	p. 383
Introduction	p. 383
Mirrors	p. 384
Sets	p. 386
Mappings	p. 387
Translations	p. 390
Rotations	p. 391
Reflections	p. 392
Glide Reflection	p. 393
Proper and Improper Transformations	p. 394
Isometries and Mirrors	p. 395
Some Reflection Exercises	p. 402
Some Additional Relations Involving Isometries	p. 403
Symmetry of the Plane	p. 405
Introduction	p. 405
The Mathematics of Symmetry	p. 408
Symmetry Groups	p. 410
Subsets of a Group	p. 411
Kaleidoscope Groups	p. 413
Pattern Generation and the Kaleidoscope	p. 415
A Colored Kaleidoscope Symmetry	p. 417
Some Other Examples of Pattern Generation	p. 419
Pattern Generation in Hyperbolic Geometry	p. 420
Line Symmetry	p. 422
The Two-Dimensional Ornamental Symmetry Groups	p. 425
Symmetry and Design	p. 430
A Fundamental Postulate	p. 432
Interaction of Two Rotocenters Implies a Third	p. 435
Nets	p. 437
Enantiomorphy	p. 438
Aesthetics of Wallpaper Patterns	p. 443
The Symmetry of Islamic Tilings	p. 445
Symmetry of Similarity	p. 446
Epilogue	p. 453
References	p. 455
Index	p. 463
Supplements	p. 473
New References for the Second Edition	p. 487
Table of Contents provided by Ingram. All Rights Reserved.