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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521728762
ISBN-139780521728768
eBay Product ID (ePID)164677144
Product Key Features
Number of Pages424 Pages
Publication NameManifold Mirrors : the Crossing Paths of the Arts and Mathematics
LanguageEnglish
SubjectPhilosophy & Social Aspects, General
Publication Year2013
TypeTextbook
Subject AreaMathematics, Art, Science
AuthorFelipe Cucker
FormatTrade Paperback
Dimensions
Item Height0.8 in
Item Weight30.5 Oz
Item Length9.7 in
Item Width6.9 in
Additional Product Features
Intended AudienceCollege Audience
LCCN2012-046405
Dewey Edition23
Reviews'Cucker [has] produced a pot au feu, an eclectic catch-all. There is much that can be learned from [his] presentation of the marriage of mathematics and art. I consider Manifold Mirrors Arcimboldesque in that it is an assemblage of many basic mathematical ideas and constructs, [adding] up to … well, to a unique work.' Philip J. Davis, SIAM News, Cucker as produced a pot au feu, an eclectic catch-all. There is much that can be learned from Cucker's presentation of the marriage of mathematics and art. I consider Philip J. Davis for SIAM News|9780521728768|
IllustratedYes
Dewey Decimal700.105
Table Of ContentMathematics: 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.
SynopsisMost 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., Felipe Cucker presents a unifying mathematical structure to explore the relationship between mathematics and the arts, including architecture, music, poetry and more. The book emerged from the author's undergraduate course, but requiring only basic high-school knowledge of mathematics it makes a fascinating read for anyone interested in the arts.