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
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
Campus Update (SUNY Oswego), September 19, 2007