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| Author | Marc Frantz, Annalisa Crannell |
|---|---|
| Publisher | Princeton University Press |
Publication date | 2011 |
| ISBN | 9780691125923 |
Viewpoints: Mathematical Perspective and Fractal Geometry in Art is a textbook onmathematics and art. It was written by mathematicians Marc Frantz andAnnalisa Crannell, and published in 2011 by thePrinceton University Press (ISBN 9780691125923). The Basic Library List Committee of theMathematical Association of America has recommended it for inclusion in undergraduate mathematics libraries.[1]
The first seven chapters of the book concernperspectivity, while its final two concernfractals and theirgeometry.[1][2] Topics covered within the chapters on perspectivity includecoordinate systems for the plane and forEuclidean space,similarity,angles, andorthocenters,one-point and multi-point perspective, andanamorphic art.[1][3] In the fractal chapters, the topics includeself-similarity,exponentiation, andlogarithms, andfractal dimension. Beyond this mathematical material, the book also describes methods for artists to depict scenes in perspective, and for viewers of art to understand the perspectives in the artworks they see,[1] for instance by finding the optimal point from which to view an artwork.[2] The chapters are ordered by difficulty, and begin with experiments that the students can perform on their own to motivate the material in each chapter.[3]
The book is heavily illustrated by artworks and photography (such as the landscapes ofAnsel Adams) and includes a series of essays or interviews by contemporary artists on the mathematical content of their artworks.[1][3]An appendix contains suggestions aimed at teachers of this material.[3]
Viewpoints is intended as a textbook for mathematics classes aimed at undergraduateliberal arts students,[1][2][4] as a way to show these students howgeometry can be used in their everyday life.[2] However, it could even be used for high school art students,[2][3]and reviewer Paul Kelley writes that "it will be of value to anyone interested in an elementary introduction to the mathematics and practice of perspective drawing".[2] It differs from many other liberal arts mathematics textbooks in its relatively narrow focus on geometry and perspective, and its avoidance of more well-covered ground in mathematics and the arts such assymmetry and the geometry ofpolyhedra.[2]
Although reviewer Blake Mellor complains that the connection between the material on perspective and on fractal geometry "feels forced", he concludes that "this is an excellent text".[4] Reviewer Paul Kelley writes that the book's "step-by-step progression" through its topics makes it "readable [and] easy-to-follow", and that "Students can learn a great deal from this book."[2] ReviewerAlexander Bogomolny calls it "an elegant fusion of mathematical ideas and practical aspects of fine art".[1]
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