Frazer Studies Interplay of Art and Math

Wills Frazer ’25 took the Hyde Chapel stage to present his work through an independent study titled “Math and Art: Parametric Cycloids, Polar Rose Curves, ​and Tessellations.”
The presentation was based on his independent study under Math Instructor Nancy Gates. Frazer, recipient of the Jefferson Scholarship at the University of Virginia, described the genesis for this topic in his study proposal:

“I used to be amused by my own proclivity for both the fields of mathematics and art. I thought that the juxtaposition of these interests was disharmonious and contradictory. However, I’ve begun to see and hope to further investigate just how intertwined these subjects are. … I hope to, under the guidance of Mrs. Gates, study the math that makes art otherwise inexplicably beautiful – what hard laws are behind visual appeal and aesthetic balance?”

Frazer used the textbook Math and Art by Sasho Kalajdzievski to study the interplay between art and math, tackling such topics as Euclidean geometry; plane transformations; perspective; and three-dimensional objects.

As part of his study, he created multiple tessellations, patterns of objects that fit together perfectly and can repeat in all directions infinitely. He cited naturally occurring shapes in nature, such as a honeycomb, and the work of M.C. Escher, whose graphic art was inspired by mathematics.

Frazer and Mrs. Gates investigated connections between mathematics and the figures generated by the Spirograph. Their goal was to generate polar rose curves (flower petal shapes) with hypotrochoids (curves traced by a fixed point on a circle rolling inside another circle) and write programs to animate them. Once they figured out how to generate a rose curve, they explored what would happen if they rotated a point on a circle around a rose curve.

“Neither Mrs. Gates nor I expected the results of what began as an interesting side quest to be so neat,” Frazer said. “It took much trial and error. There was a period where I was sure that we would not figure it out, but it’s really nice now to run the final program and see the smooth, esthetically pleasing curves generated by these rotations.”

Frazer plans to submit his work for the 2025 Steven H. Strogatz Prize for Math Communication at the National Museum of Mathematics in New York City. Winners receive cash prizes and are recognized online.
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