Review of "Viewpoints: Mathematical Perspective and Fractal Geometry in Art," by Marc Frantz and Annalisa Crannell

Review of

Viewpoints: Mathematical Perspective and Fractal Geometry in Art, by Marc Frantz and Annalisa Crannell, Princeton University Press, Princeton, New Jersey, 2011. 248 pp., $52.00 (hardbound). ISBN 9780691125923

This is a textbook/workbook that blends both art and mathematics while not skimping on either one. Tactics such as perspective and viewpoints are demonstated using both illustrations and the equations that describe them. It is designed for courses in mathematics for liberal arts, mathematics for artists and other interdisciplinary courses where art and mathematics are combined.

 An artist’s vignette follows each chapter and one of the common themes is that when the experienced artists are exposed to the mathematical explanations for the first time they recognize that the formulas represent what they have been doing all along. The mathematics is essentially applied geometry, there is a bit of algebra but it is all directly related to what appears in the drawings and images. This makes it much easier for the reader/student to understand the purpose and consequences of the equations.

 The chapter titles are as follows:

*) Introduction to Perspective and Space Coordinates

*) Perspective by the Numbers

*) Vanishing Points and Viewpoints

*) Rectangles in One-Point Perspective

*) Two-Point Perspective

*) Three-Point Perspective and Beyond

*) Anamorphic Art

*) Introduction to Fractal Geometry

*) Fractal Dimension

Each chapter closes with a set of exercises and solutions to many are included in an appendix.

 As can be seen from the content of this book, mathematics is the foundation of quality art, the discovery and application of perspective led to a dramatic change in the realistic nature of painting. This book is a textbook in the traditional format and is also a strong response to the question, “What is math used for anyway?”

This book was made available for free for review purposes

http://press.princeton.edu/titles/9496.html