Frank A. Farris teaches mathematics at Santa Clara University and is a former editor of Mathematics Magazine, a publication of the Mathematical Association of America. He is also the author of the new Princeton University Press book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. The book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry.
Frank Farris gave Princeton University Press a look at why he wrote Creating Symmetry, where he feels this book will have major contributions, and what comes next.
What inspired you to get into mathematical writing?
FF: After editing Mathematics Magazine for many years, I developed a passion for communicating mathematics: I didn’t want dry accounts written by anonymous authors; I wanted stories told by people. I wasn’t so interested in problems and puzzles, but in the stories that bring us face to face with the grand structures of mathematics.
Why did you write this book?
FF: Many years ago, I asked the innocent question: What is a wallpaper pattern, really? Creating Symmetry is the story of my dissatisfaction with standard answers and how it led me on a curious journey to a new kind of mathematical art. I took some risks and let my personality show through, while maintaining an honest, mathematically responsible approach. I hope readers enjoy the balance: real math told by a person.
What do you think is the book’s most important contribution?
FF: Most people who see my artwork say they’ve never seen anything like these images and that pleases me immensely. Of course, people have seen wallpaper patterns before, but the unusual construction method I use—wallpaper waves and photographs—gives my patterns an intricacy and rhythm that people wouldn’t create through the usual potato-stamp construction method, where the patterns is made from discrete blocks.
What is your next project?
FF: I am working on a “wallpaper lookbook,” a book for the simple joy of looking at patterns. Creating Symmetry tells people how to make the patterns, and there’s quite a lot of mathematical detail to process. Not everyone who likes my work wants to know all the details, but can still appreciate the “before and after” nature of the images.
Who do you see as the audience for this book?
FF: There are three audiences and they will read the book in different ways. The general reader, who knows some calculus but may be a little rusty, should find a refreshing and challenging way to reconnect with mathematics. Undergraduate mathematics majors will enjoy the book as a summer project or enrichment reading, as it makes surprising connections among topics they may have studied. The professional mathematician will find this light reading—a chance to enjoy the amazing interconnectedness of our field.