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Manifold Mirrors: The Crossing Paths of the Arts and Mathematics [Paperback]

Felipe Cucker

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Book Description

25 April 2013 0521728762 978-0521728768
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.

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'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

'… there is certainly something new to be discovered for every reader. The book grew out of a course, and so it is obviously possible to extract some interesting lectures from the material that is presented.' The European Mathematical Society (

'The merits of this big, ambitious book greatly exceed its deficiencies. Felipe Cucker's immense learning, and his often densely technical presentation of mathematical complexities, are balanced by a pervasive lightness of tone and by a flair for offbeat allusions that range from Euripides to Busby Berkeley. His book is a joy for the eye and a feast for the mind.' Hardy Grant, MAA Reviews

Book Description

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.

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5.0 out of 5 stars Symmetry throughout the Arts (painting, poetry, music, etc.) 30 Jan 2014
By Pichierri Fabio - Published on
The book of Cucker, a professor of mathematics, explores the role of symmetry in the arts (painting, poetry, music, etc.). Because symmetry is part of geometry, the introductory chapters discuss many important concepts (eg. isometry of the plane, symmetry elements and operations, etc.) which are utilized throughout the book. Several works of art are analyzed in detail, such as (at the beginning) the beautiful fresco "Majesty" of Simone Martini (1284-1344) displayed in Siena which shows an interesting (pseudo)mirror symmetry and the famous Raphael's fresco "The School of Athens" (on the book's cover) which represents an elegant example of one-point perspective with the "intrusion" of a two-point perspective element (I wonder how many people recognized it, I didn't). More complex geometrical constructs are encountered in the graphic art of Maurits Escher, my favorite modern artist. Examples from poetry (Milton, Borges) and music (Bela Bartok) are also discussed in the book which is likely to appeal to a wide audience of people interested in discovering the interplay between math and the arts.
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