"Honorable Mention for the 2016 PROSE Award in Mathematics, Association of American Publishers" 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 step-by-step illustrated introduction to the astounding mathematics of symmetry
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. "[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 "This is clearly a book which will appeal to mathematicians with an aesthetic bent as well as to artists who want to employ both mathematics and computer-generated technology. The book is attractively priced and would grace any school or departmental library."---Gerry Leversha, Mathematical Gazette "For the mathematically educated reader, Frank Farris' book, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, gives some sage guidance . . . with 27 beautiful vignettes of art generated by complex-valued functions along with explanations that cover just enough mathematics to explain what is going on without getting overly fussy about the technical details." "Frank's rich artistry vibrantly enlivens the mathematics of symmetry. What a treat for the eye and the mind
