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Viewpoints: Mathematical Perspective and Fractal Geometry in Art
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students.
Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.
Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.
- GenresArt
248 pages, Paperback
First published July 5, 2011
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About the author
Marc Frantz
3 booksMarc Frantz is a research associate in mathematics at Indiana University. He holds a BFA in painting from the Herron School of Art and an MS in mathematics from Purdue University.
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Displaying 1 of 1 review
January 15, 2016
The perfect textbook for courses in the application of mathematics to art
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 and this review also appears on Amazon
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 and this review also appears on Amazon
Displaying 1 of 1 review