Artful Geometry

Math professor's online book links geometry to art, aesthetics

Dr. George Baloglou of SUNY Oswego's mathematics department explores how geometry inspires art, architecture and so-called wallpaper patterns with his recently launched online book "Isometrica."

The book evolved out of Math 103, "Symmetries," a general education course created by Dr. Margaret Groman in 1992. Baloglou has taught it since 1995. He said he became interested in doing the book the first time he taught the course.

"If you go to the literature, you will see this topic generally is treated more abstractly, more algebraically, while I stress geometry," Baloglou said. "I wanted something that would be accessible to the average student but also of some interest to the average mathematician."

A major thrust is to show how geometry plays out in everyday objects and regular activities. If you picture a set of parallel, mirrored footsteps, you would see something called a "glide reflection," a type of mathematical transformation crucial in Math 103, Baloglou said.

He also views geometrical patterns with an eye toward aesthetics. One example would be renowned artist M.C. Escher, known for his intricate mathematics-inspired works. "I'm interested in Escher's symmetry, but not his tiling," or repetition of real-world objects, Baloglou said.

The first six chapters are covered in the course, with the last two chapters devoted to more advanced work with "the goal of demonstrating that there are only 17 ways to create wallpaper designs," Baloglou explained, adding that other authors prove this theory from an algebraic, not geometric, angle.

"I believe the presentation of this material in most authors' books is kind of cold," he said. "For other authors, it's just a chapter in a book they put in just to address the topic. For me, this is the focus of the whole book."

As opposed to treating the subject dryly, he wrote it in the second person ("you") as if engaging the reader in a conversation.

His unconventional approach includes making the book available for free on the Internet, thus sparing Math 103 students having to buy one more textbook as well as making it available to anyone in the world with an Internet connection. "They don't have to spend any money on it, only invest their time and energy," he said.

Some of the chapters have been on the Web for years, but Baloglou recently assembled the book in sequenced form, including an introduction and two final chapters. Baloglou monitors the traffic on his book and related Web material, estimating that a precursory site titled "Crystallography Now," an informal classification of the 17 wallpaper patterns, has been visited more than 20,000 times since first launched in April 2002.

"In the end, it may be more a teacher's or a mathematician's book than a student's, but if a student becomes interested in this, it's very readable and accessible," Baloglou said.

The book is heavy on visuals, and Baloglou estimated it took around eight months of writing between 1998 and 2001, but it seemed more like a labor of love. "It was fun creating the pictures and writing the book," he said.

More information and a downloadable version of the book can be found at

Tim Nekritz

Campus Update (SUNY Oswego), September 19, 2007