E-Book 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: Instructors manual (available only to teachers)
E-Book Content
VIEWPOINTS
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VIEWPOINTS Mathematical Perspective and Fractal Geometry in Art Marc Frantz Annalisa Crannell
Princeton University Press Princeton and Oxford
c 2011 by Princeton University Press Copyright Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire, OX20 1TW press.princeton.edu Cover photo: Winter Road along the Trees, by Wil Van Dorp All Rights Reserved Library of Congress Cataloging-in-Publication Data Frantz, Marc, 1951– Viewpoints: mathematical perspective and fractal geometry in art / Marc Frantz, Annalisa Crannell. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12592-3 (hardback: alk. paper) 1. Perspective—Textbooks. 2. Fractals—Textbooks. 3. Art—Mathematics—Textbooks. I. Crannell, Annalisa. II. Title. QA515 .F73 2011 742.01′51-dc22 2010053315 British Library Cataloging-in-Publication Data is Available This book has been composed in LATEX The publisher would like to acknowledge the authors of this volume for providing the camera-ready copy from which this book was printed. Printed on acid-free paper. ∞ Printed in the United States of America 1 3 5 7 9 10 8 6 4 2
Contents Preface
vii
Acknowledgments
ix
1 Introduction to Perspective and Space Coordinates Artist Vignette: Sherry Stone 2 Perspective by the Numbers
1 9 13
Artist Vignette: Peter Galante
25
3 Vanishing Points and Viewpoints
29
Artist Vignette: Jim Rose 4 Rectangles in One-Point Perspective What’s My Line?: A Perspective Game 5 Two-Point Perspective Artist Vignette: Robert Bosch 6 Three-Point Perspective and Beyond Artist Vignette: Dick Termes 7 Anamorphic Art Viewpoints at the Movies: The Hitchcock Zoom
39 43 55 59 77 85 113 117 135
Plates follow page 138 8 Introduction to Fractal Geometry
139
vi
Contents Artist Vignette: Teri W