Math Project - Knot Theory

 Our group - Manveen, Caris, Krystal, and Jasmine

Recreated Holly Laws's "Trefoil Knot" using clay and discussed Knot Theory as a branch of topology in our presentation. We introduced key concepts like knot invariants and tricolorability. Knot invariants remain topologically equivalent through simple transformations such as stretching, bending, twisting, or shrinking. Tricolorability, a tool for identifying these invariants, refers to the ability of a knot to be coloured with three distinct colors, where each uninterrupted chain is one color, and each intersection has either all three or just one color. In our model, one side demonstrated tricolorability, while the other side reflected Holly Laws’s original choice of colors and materials. Additionally, we highlighted the cultural, scientific, and everyday significance of knots, noting how knot theory models DNA replication, helping visualize and predict the complex topological structures of DNA. As part of our activity, we provided clay and strings for classmates to create their own trefoil knots, challenging them to explore transformations that preserve topological equivalence. This hands-on approach deepened our understanding and reinforced the value of incorporating interactive activities into classroom teaching to help students grasp abstract concepts.

The challenge for me is getting a deeper understanding of Knot theory which happens everywhere in our real life, but I am not very sensitive to geometry and space, so it’s also a very good way for me to learn more about knot theory and try my best to make it easier to explain and understand for our listeners (classmates). Also, I’m very happy that my group has come up with a lot of good ideas, like reproducing the art project by clay, and we had a very productive process.

Having an activity during the class is a very good way to build connections with students and make students engaged in the class. Also, we could find some real life examples for students to know more about the knowledge and get them interested. What’s more, Math could be related with other subjects. For example, knot theory could be related with physics, biology and arts, for some knowledge in math history such as the golden ratio could be related with Arts and Geography.