Manifold Mirrors
The Crossing Paths of the Arts and Mathematics

This fascinating book will interest anyone wanting to learn more about the relationship between mathematics and the arts.

Felipe Cucker (Author)

9780521429634, Cambridge University Press

Hardback, published 25 April 2013

426 pages, 55 b/w illus. 100 colour illus. 30 music examples
24.4 x 17 x 2.4 cm, 0.88 kg

'This is an impressive and ambitious book and is one well-worth taking time to work through.' Richard Talbot, Nexus Network Journal

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.

Mathematics: user's manual
Appetizers
1. Space and geometry
2. Motions on the plane
3. The many symmetries of planar objects
4. The many objects with planar symmetries
5. Reflections on the mirror
6. A raw material
7. Stretching the plane
8. Aural wallpaper
9. The dawn of perspective
10. A repertoire of drawing systems
11. The vicissitudes of perspective
12. The vicissitudes of geometry
13. Symmetries in non-Euclidean geometries
14. The shape of the universe
Appendix: rule-driven creation
References
Acknowledgements
Index of symbols
Index of names
Index of concepts.

Subject Areas: Geometry [PBM], Mathematics [PB], Theory of music & musicology [AVA], Theory of art [ABA], The arts [A]