W&L Professor Publishes Article On Geometric Design
Greg Dresden, professor of mathematics at Washington and Lee University, recently produced an article and accompanying illustrations that were published in the May 2025 edition of The College Mathematics Journal.
In the article “Epitrochoids and Hypotrochoids Together Again,” Dresden reveals mathematical insights into two classic geometric curves, demonstrating how complex mathematics can create beautiful and unexpected patterns that are both scientifically intriguing and visually stunning.
The article explores epitrochoids and hypotrochoids, which are intricate geometric shapes that emerge when one circle rolls around the outside or inside of another circle. What makes his research unique is an innovative approach of using complex variables to unlock these curves’ hidden symmetries and then putting the two distinct types of curves onto the same graph at the same time.
“These curves have been studied and written about for 500 years, and yet, until now, nobody thought of putting them together and looking at the complex and complicated ways that they intersect with themselves and with each other,” Dresden said. “There’s a lot of hidden symmetry that’s just waiting to be discovered.”
Dresden’s work isn’t just about abstract mathematics. It demonstrates how mathematical exploration can reveal unexpected beauty in geometric forms, bridging the gap between pure mathematics and artistic design.
“I knew that my article was scheduled to appear in this month’s issue, but it was quite a surprise when I got it in the mail and saw that the editors also chose my pictures for the cover,” he said. “It’s quite an honor, and it all started with me writing up some test questions for my students in Math 221.”
Dresden has been a member of the W&L faculty since 1997, serving as chair of the mathematics department from 2011 to 2015 and again in 2021. He has been a member of numerous committees, including the Financial Aid Committee, Courses and Degrees Committee, Automatic Rule and Readmission Committee, the Teaching Program Advisory Group and the Technology Task Force. He holds a bachelor of science in mathematics from Stanford University, a master of arts in mathematics from the University of Wisconsin-Madison and a doctorate in mathematics from the University of Texas at Austin.
