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Geometric Design Students Combine Mathematics and Art

by ASMS math professor Sarah Brewer

Hannah Nguyen
Indomalayan biomorphic pattern by junior Hannah Nguyen

During Winter Term, I was finally able to offer an entire elective course centered around my mathematical and artistic research: the Euclidean construction of historic Islamic geometric patterns. Students in my Visual Mathematics class, various AIMS classes, previous Special Projects, and Directed Research students have been able to study these patterns with me, but never at this level.

We were really able to dig deep into the algorithms behind the construction of star rosette patterns, making use of geometric theorems to construct beautiful, intricate designs. It’s a project-based class, so students learn by doing. Applying the inscribed angle theorem is a lot more fun when it’s in the context of drawing a star polygon that meets certain criteria than when you’re just trying to solve for x and that’s it. We also got to explore a lot of media. Students drew with traditional compass and straightedge, folded patterns with origami, and constructed them on a computer with Geogebra. This group’s final projects were especially good. They were tasked with choosing a pattern found “in the wild,” reconstructing that pattern in their medium of choice, researching the building the pattern is found in as well as the city and greater historical context, and presenting their work and findings to the class.

I look forward to offering this course again next school year and sharing all of the new ideas I’ve gained through the regular research discussions I have with experts all over the world.

Click here to check out the awesome presentations from this year’s class: https://youtu.be/Q_iPeE5SZa4

Senior Isabelle Stabler says, “I replicated a pattern that can be found only in the Great Mosque of Damascus, in Damascus Syria. The mosque has been a religious symbol in Syria since 714 AD, and holds many other beautiful mosaics and patterns. Throughout the term we learned how to create these patterns in an online program, Geogebra, along with ruler and compass so I’ve used both to produce my pattern. I’ve loved taking geometric design, and couldn’t have been happier with how we needed the class!”

Katherine Rutschilling studied a 12-fold pattern from Multan, Pakistan. “I have really enjoyed this class and the chance it gave me to express myself in a way I wouldn't normally try. I took this class because I thought it would take me out of my comfort zone, and it ended up being my favorite class this term.”

Pattern from the Alhambra in Granada, Spain by sophomore Marlan Zha

Pattern from the Agra Fort in Agra, India by junior Nathan Kim

Pattern from the Agra Fort in Agra, India by senior Sammie Neno

Pattern from Itman-ud-Daulah’s Tomb in Agra, India by senior Alexandria Sessions

  • Mar 12, 2021