Viewpoints: Mathematical Perspective and Fractal Geometry in Art

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Overview

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.

  • Classroom-tested activities and problem solving
  • Accessible problems that move beyond regular art school curriculum
  • Multiple solutions of varying difficulty and applicability
  • Appropriate for students of all mathematics and art levels
  • Original and exclusive essays by contemporary artists
  • Forthcoming: Instructor's manual (available only to teachers)
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Editorial Reviews

Cut the Knot
The book goes a long way trying to convey to its audience—through both theory and practice—professional techniques that could not fail but empower students to make accurate, sophisticated drawings. The book presents an elegant fusion of mathematical ideas and practical aspects of fine art.
Journal of Mathematics and the Arts
[T]his is an excellent text that I will certainly consider using for a future class. The material on perspective is accessible, thorough and well-written, and the text is designed for a hands-on pedagogy that is well-suited to the intended audience. And as an elementary, but thorough, discussion of both the mathematics and practice of perspective drawing, it deserves a place in any collection of books on mathematics and the arts.
— Blake Mellor
Choice
The writing is extremely clear, the material is fresh, and the many excellent diagrams clarify the ideas under discussion. The authors use relevant artwork to illustrate the mathematical principles. . . . The exercises are original and promote active learning. . . . This is an excellent work for academic curricula and an outstanding resource for self-study in mathematical perspective, fractals, and the relationship between art and mathematics.
Journal of Mathematics and the Arts - Blake Mellor
[T]his is an excellent text that I will certainly consider using for a future class. The material on perspective is accessible, thorough and well-written, and the text is designed for a hands-on pedagogy that is well-suited to the intended audience. And as an elementary, but thorough, discussion of both the mathematics and practice of perspective drawing, it deserves a place in any collection of books on mathematics and the arts.
From the Publisher

"The book goes a long way trying to convey to its audience--through both theory and practice--professional techniques that could not fail but empower students to make accurate, sophisticated drawings. The book presents an elegant fusion of mathematical ideas and practical aspects of fine art."--Cut the Knot

"[T]his is an excellent text that I will certainly consider using for a future class. The material on perspective is accessible, thorough and well-written, and the text is designed for a hands-on pedagogy that is well-suited to the intended audience. And as an elementary, but thorough, discussion of both the mathematics and practice of perspective drawing, it deserves a place in any collection of books on mathematics and the arts."--Blake Mellor, Journal of Mathematics and the Arts

"The writing is extremely clear, the material is fresh, and the many excellent diagrams clarify the ideas under discussion. The authors use relevant artwork to illustrate the mathematical principles. . . . The exercises are original and promote active learning. . . . This is an excellent work for academic curricula and an outstanding resource for self-study in mathematical perspective, fractals, and the relationship between art and mathematics."--Choice

"This is not a book to read passively and, indeed, you will want to read this book with a pencil in hand. The text is designed to be experienced first hand, sketching out examples whilst following the text, as well as doing the exercises at the end of each chapter that develop the material well. . . . Prerequisites for this book are a minimum, effectively being an understanding of basic coordinate geometry. I would recommend this book to anyone who is interested in the interplay between mathematics and art."--George Matthews, Mathematics Today

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Product Details

  • ISBN-13: 9780691125923
  • Publisher: Princeton University Press
  • Publication date: 7/25/2011
  • Pages: 258
  • Sales rank: 1,057,030
  • Product dimensions: 8.00 (w) x 10.00 (h) x 2.06 (d)

Meet the Author

Marc Frantz holds a BFA in painting from the Herron School of Art and an MS in mathematics from Purdue University. He teaches mathematics at Indiana University, Bloomington where he is a research associate. Annalisa Crannell is professor of mathematics at Franklin & Marshall College. She is the coauthor of "Writing Projects for Mathematics Courses".

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Table of Contents

Preface vii
Acknowledgments ix

Chapter 1: Introduction to Perspective and Space Coordinates 1
Artist Vignette: Sherry Stone 9

Chapter 2: Perspective by the Numbers 13
Artist Vignette: Peter Galante 25

Chapter 3: Vanishing Points and Viewpoints 29
Artist Vignette: Jim Rose 39

Chapter 4: Rectangles in One-Point Perspective 43
What’s My Line?: A Perspective Game 55

Chapter 5: Two-Point Perspective 59
Artist Vignette: Robert Bosch 77

Chapter 6: Three-Point Perspective and Beyond 85
Artist Vignette: Dick Termes 113

Chapter 7: Anamorphic Art 117
Viewpoints at the Movies: The Hitchcock Zoom 135
Plates follow page 138

Chapter 8: Introduction to Fractal Geometry 139
Artist Vignette: Teri Wagner 157

Chapter 9: Fractal Dimension 161
Artist Vignette: Kerry Mitchell 193
Answers to Selected Exercises 197

Appendix: Information for Instructors 215
Annotated References 223
Index 229

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