At first blush, art and math couldn’t seem more different from one another: free-flowing creative expression versus rigid rule-based analysis. But the histories of the two disciplines are deeply intertwined. The mathematicians of the medieval Middle East developed algebra and represented the patterns they found there in woven tapestries and mosaic tessellations. Tessellation is the creation of a two-dimensional plane with regular and repeating geometric shapes that fit together with no overlaps and no gaps, like the tiles of a bathroom floor.

Radmila Sazdanovic, a postdoctoral researcher in the Department of Mathematics in the School of Arts and Sciences, puts a modern spin on this tradition. As a mathematician, she studies theoretical spaces and surfaces. As an artist, she applies this knowledge to make swirling patterns imbued with subtle symmetries and geometric elegance.

A collection of her work, “Fisheye View of Mathematics,” is on display and available for purchase at the Burrison Gallery in the University Club at Penn, 3611 Walnut St. The exhibit is on display through April 6. 

Sazdanovic’s art uses hyperbolic geometry, rather than Euclidean geometry, which is especially relevant for tessellations. While four square tiles come together at a single point on your bathroom floor, an Euclidean plane, more shapes can fit neatly together in a hyperbolic plane.  

Using a computer program called Tess, which she and her colleagues wrote in 2002, Sazdanovic generates algorithms that weave shapes of her choosing into hyperbolic tessellations. They extend infinitely in all directions, but are represented in our Euclidean world as circles, where the pattern shrinks as it approaches the edge, hence the “fisheye” in her exhibit’s name.

Sazdanovic then uses another program to select patterns within the tessellation, which she represents with additional shapes and colors.

Sazdanovic’s work is not just about pretty pictures, however. Her involvement in the world of mathematical art led to her becoming coeditor of the electronic journal Visual Mathematics.

"The relationship between math and art is a two-way street," she says. “You can use math to make something aesthetically pleasing, but also use that art to convey a mathematical idea that would take pages and pages of formulas and symbols.” 

The Burrison Gallery is open Monday through Friday, 7:30 a.m. to 5 p.m., and Saturday and Sunday, 7 a.m. to 1 p.m.