Viewpoints

Mathematical Perspective and Fractal Geometry in Art
Erscheinungsjahr 2011
ISBN: 978-0-691-12592-3
Verlag: Princeton University Press

Buch, Englisch, 258 Seiten, Format (B × H): 208 mm x 260 mm, Gewicht: 787 g

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 Solutions manual (available only to teachers)

Autoren/Hrsg.

Frantz, Marc

Crannell, Annalisa

Fachgebiete

• Geisteswissenschaften Kunst Kunst, allgemein
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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

Über Autor(innen)

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".