Connections: The Geometric Bridge Between Art & Science (2nd Edition)

by Jay Kappraff

Overview

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.

Product Details

ISBN-13:	9789810245863
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	11/29/2001
Series:	Series On Knots And Everything , #25
Edition description:	Second Edition
Pages:	520
Product dimensions:	6.00(w) x 8.50(h) x 1.10(d)

Table of Contents

Preface     xi
Acknowledgements     xv
Credits     xvii
Preface to the Second Edition     xxiii
Proportion in Architecture     1
Introduction     1
Myth and Number     2
Proportion and Number     7
The Structure of Ancient Musical Scales     9
The Musical Scale in Architecture     12
Systems of Proportion Based on [radical]2, [theta], and [phi]     16
The Golden Mean and Its Application to the Modulor of Le Corbusier     21
An Ancient System of Roman Proportion     28
Appendix 1.A     32
Similarity     35
Introduction     35
Similarity     36
Families of Similar Figures     37
Self-Similarity of the Right Triangle     38
Line Choppers     41
A Circle Chopper     41
Construction of the Square Root of a Given Length     43
Archimedes Spiral     44
Logarithmic Spiral     45
Groth and Similarity in Nature     48
Growth and Similarity in Geometry     52
Infinite Self-Similar Curves     55
On Growth and Form     63
Appendix2.A     65
Appendix 2.B     67
The Golden Mean     75
Introduction     75
Fibonacci Series     76
Some Tiling Properties of [phi]     81
The Golden Rectangle and the Golden Section     82
The Golden Mean Triangle     85
The Pentagon and Decagon     86
The Golden Mean and Patterns of Plant Growth     89
The Music of Bartok: A System Both Open and Closed     97
Graphs     105
Introduction     105
Graphs     108
Maps     114
Maps and Graphs on a Sphere     117
Connectivity of Graphs and Maps     119
Combinatorial Properties     120
Regular Maps     122
New Graphs from Old Ones     124
Duality     125
Planar and Nonplanar Graphs     127
Maps and Graphs on Other Surfaces     129
The Torus and the Moblus Strip     134
Magic Squares     137
Map Coloring     138
Regular Maps on a Torus     141
Szilassi and Csaszar Maps     142
Floor Plans     145
Bracing Structures     154
Eulerian Paths     159
Hamiltonian Paths     163
Tilings with Polygons     167
Introduction     167
Polygons     169
Regular Tilings of the Plane     173
Duality     177
Semiregular Tilings     177
Symmetry     178
Duality of Semiregular Tilings     181
The Module of a Semiregular Tiling     182
Other Tilings with Regular Polygons     183
Transformations of Regular Tiling     183
Nonperiodic Tilings     194
Origami Patterns     198
Islamic Art     200
Two-Dimensional Networks and Lattices     209
Introduction     209
Planar Soap Films     209
Random Cellular Networks     214
Rural Market Networks     217
Dirichlet Domains     220
Spider Webs, Dirichlet Domains, and Rigidity     224
Lattices     230
Pattern Generation with Lattices     234
Dirichlet Domains of Lattices and Their Relation to Plant Growth     238
Quasicrystals and Penrose Tiles     243
Projective Geometry     248
Polyhedra: Platonic Solids      255
Introduction     255
The Platonic Solids     257
The Platonic Solids as Regular Polyhedra     259
Maps of Regular Polyhedra on a Circumscribed Sphere     261
Maps of the Regular Polyhedra on the Plane-Schlegel Diagrams     263
Duality     264
Combinatorial Properties     268
Rigidity     270
The Angular Deficit     273
From Maps to Polyhedra-The Dihedral Angle     275
Space-Filling Properties     277
Juxtapositions     279
Symmetry     282
Star Polyhedra     288
Duals     291
A Proof of Descartes Formula     292
Appendix 7.C
Transformation of the Platonic Solids I     295
Introduction     295
Intermediate Polyhedra     296
Interpenetrating Duals Revisited     299
The Rhombic Dodecahedron     301
Embeddings Based on Symmetry     303
Designs Based on Symmetry Breaking     306
Relation to the Golden Mean     308
Tensegrities     310
The Tetrahedron-Methane Molecule Molecule and Soap Bubble     313
Tetrahedron as the Atom of Structure     315
Packing of Spheres     317
Geodesic Domes and Viruses     323
Transformation of the Platonic Solids II     327
Introduction     327
Archimedean Solids     327
Truncation     329
The Truncated Octahedron     332
The Snub Figures     334
Archimedean Duals     335
Maps on a Sphere     335
Combinatorial Properties     337
Symmetry Revisited     339
Prisms and Antiprisms     341
Polyhedra: Space Filling     347
Introduction     347
Close Packing of Spheres     347
The Shape of Space     350
Packing Ratios     353
Three-Dimensional Lattices     355
Dirichlet Domains     356
Crystal Structure     357
Networks     360
Infinite Regular Surfaces     362
The Diamond and Graphite Nets     365
Soap Froths     368
A Unified Look at Nets Related to Cubic Lattices     369
Zonohedra     371
Golden Isozonohedra     377
Isometries and Mirrors     383
Introduction     383
Mirrors      384
Sets     386
Mappings     387
Translations     390
Rotations     391
Reflections     392
Glide Reflection     393
Proper and Improper Transformations     394
Isometries and Mirrors     395
Some Reflection Exercises     402
Some Additional Relations Involving Isometries     403
Symmetry of the Plane     405
Introduction     405
The Mathematics of Symmetry     408
Symmetry Groups     410
Subsets of a Group     411
Kaleidoscope Groups     413
Pattern Generation and the Kaleidoscope     415
A Colored Kaleidoscope Symmetry     417
Some Other Examples of Pattern Generation     419
Pattern Generation in Hyperbolic Geometry     420
Line Symmetry     422
The Two-Dimensional Ornamental Symmetry Groups     425
Symmetry and Design     430
A Fundamental Postulate     432
Interaction of Two Rotocenters Implies a Third     435
Nets     437
Enantiomorphy     438
Aesthetics of Wallpaper Patterns     443
The Symmetry of Islamic Tilings     445
Symmetry of Similarity     446
Epilogue     453
References     455
Index     463
Supplements     473
New References for the Second Edition     487

Editorial Reviews

Kappraff (math, New Jersey Institute of Technology) illustrates how the properties of symmetry, proportion, connectivity, and stability are involved in the creation of beautiful designs, structures, and objects--how mathematics serves as a foundation of design science. Accessible to non-mathematicians. Useful as a text for design courses. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

This is a new edition of a reference that brings together material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry in order to demonstrate that the grammar of space can be the basis of a common language that spans the scientific and artistic worlds. Kappraff (New Jersey Institute of Technology) presents 12 chapters that discuss both theory and practice. New material includes a supplementary section that contains the recent work of Haresh Lalvani, as well as additional material on the snub figure, uniform polyhedra, and the Dorman Luke method of constructing the faces of dual polyhedra. Can be used both by professionals and as a textbook. Contains about 750 b&w illustrations. Annotation c. Book News, Inc., Portland, OR (booknews.com)