Manifold Mirrors: The Crossing Paths of the Arts and Mathematics by Felipe CuckerManifold Mirrors: The Crossing Paths of the Arts and Mathematics by Felipe Cucker

Manifold Mirrors: The Crossing Paths of the Arts and Mathematics

byFelipe Cucker

Hardcover | June 28, 2013

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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.
Title:Manifold Mirrors: The Crossing Paths of the Arts and MathematicsFormat:HardcoverDimensions:424 pages, 9.72 × 6.85 × 0.91 inPublished:June 28, 2013Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521429633

ISBN - 13:9780521429634

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Table of Contents

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.