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Manifold Mirrors - The Crossing Paths of the Arts and Mathematics
by Felipe Cucker
Cambridge University Press | June 2013 | ISBN-10: 0521728762 | PDF | 424 pages | 46.6 mb
http://www.amazon.com/Manifold-Mirrors-Crossing-Paths-Mathematics/dp/0521728762
Most works of art, whether illustrative, musical or literary, are created subject to a set of constraints. In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J. S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides both a development in geometry and a description of how these frameworks fit the creative process within several art practices. He furthermore discusses the perceptual effects derived from the presence of particular geometric characteristics. The book began life as a liberal arts course and it is certainly suitable as a textbook. However, anyone interested in the power and ubiquity of mathematics will enjoy this revealing insight into the relationship between mathematics and the arts.
About the Author
Felipe Cucker is Chair Professor of Mathematics at the City University of Hong Kong. His research covers a variety of subjects including semi-algebraic geometry, computer algebra, complexity, emergence in decentralized systems (in particular, emergence of languages and flocking), learning theory, and foundational aspects of numerical analysis. He serves on the editorial board of several journals and is Managing Editor of the journal Foundations of Computational Mathematics, published by the society of the same name.
CONTENTS
Mathematics: user’s manual page ix
Appetizers 1
1 Space and geometry 11
2 Motions on the plane 27
3 Themany symmetries of planar objects 39
4 Themany objects with planar symmetries 83
5 Reflections on the mirror 111
6 A raw material 128
7 Stretching the plane 158
8 Aural wallpaper
9 The dawn of perspective 225
10 A repertoire of drawing systems 260
11 The vicissitudes of perspective 293
12 The vicissitudes of geometry 321
13 Symmetries in non-Euclidean geometries 357
14 The shape of the universe 373
Appendix: Rule-driven creation 381
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