Manifold Mirrors: The Crossing Paths of the Arts and Mathematics by Felipe Cucker (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A really wonderful book. The discussion of plane symmetries is first-rate

⭐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.

⭐Excellently produced book, especially the illustrations

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