This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics.
Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own.
Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.
Frank A. Farris teaches mathematics at Santa Clara University. He is a former editor of Mathematics Magazine, a publication of the Mathematical Association of America. He lives in San Jose, California.
"[A] beautifully illustrated guide to fusing mathematical and artistic creativity to generate fascinating and visually appealing designs."--Evelyn Lamb, Scientific American
"[A] beautiful book. . . . [Creating Symmetry] is a thoughtful, innovative and interesting piece of work, discussing material that the author is obviously very enthusiastic about; such enthusiasm is, as is often the case, contagious."--Mark Hunacek, MAA Reviews
"This is a marvelous book that brings groups, and along the way many other mathematical concepts, to the reader in an unconventional way."--Adhemar Bultheel, European Mathematical Society Bulletin
"Mathematics students thus get a visually rich path into group theory that compellingly informs even first steps with ideas usually deemed advanced. Braver art students will find motivation and the means to learn some mathematics they can put right to use."--D. V. Feldman, Choice
"[A] delightful showcase of artistic applications of complex wave functions. . . . This attractive book will appeal to and inspire a broad range of practitioners including complex analysts, mathematical artists, and advanced undergraduates."--Heidi Burgiel, College Mathematics Journal
"Frank's rich artistry vibrantly enlivens the mathematics of symmetry. What a treat for the eye and the mind!"--Michael Starbird, The University of Texas at Austin
"The imagery in this book is attractive and engaging, and illustrates Farris's excellent command of the mathematical techniques and his strong sense of visual design. General readers will appreciate the beauty of the images and will find incentive to learn how mathematics can be used in creative ways to produce art."--George W. Hart, coauthor of Zome Geometry: Hands-on Learning with Zome Models
Table of Contents
Click to enlarge
Click to enlarge
Click to enlarge