Abstract
Most people imagine advanced math as endless calculus classes or solving increasingly complicated equations. However, advanced mathematics also includes the study of knots—the same ones used to tie our shoes. In fact, the loop of a ponytail holder is one of the simplest mathematical knots. Would students sleep through math if they were learning about rope magic tricks? Knot theory, a branch of topology, is the study of closed curves. Despite it being considered an advanced topic, many of its fundamental concepts are accessible to high school students. Given the flexibility in New York State high school math graduation requirements, math educators have opportunities to introduce engaging nontraditional topics that can help change students’ perspectives regarding mathematics. To help educators bring this exciting topic into their classrooms, this capstone features hands-on, inquiry-based instructional materials, which foster curiosity and critical thinking. These activities have been developed using principles of inquiry-based learning with a focus on collaboration and gamification. Why knot theory? Beyond being a fun topic, knot theory has applications in fields like biology, physics, and computer science, showing students the diverse ways mathematics shapes our world. But do knot worry if this all sounds complicated; it is not as knotty as it seems!
Recommended Citation
Bunster, Jocelyn
(2026)
"Knot Your Average Math Class: Exploring Curves and Curiosities,"
Proceedings of GREAT Day: Vol. 17, Article 12.
Available at:
https://knightscholar.geneseo.edu/proceedings-of-great-day/vol17/iss1/12