Math Art project reflection

Our group - Manveen, Caris, Krystal, and I - 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 colours, where each uninterrupted chain is one colour, and each intersection has either all three or just one colour. In our model, one side demonstrated tricolorability, while the other side reflected Holly Laws’s original choice of colours and materials. To expand on the use of knots, 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. Moreover, to pique further interest, we talked about the importance of Knot Theory in understanding the behaviours of various diseases related to protein aggregation such as Alzheimers, as well as, knots in higher dimensions. 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.

This project challenged me to delve into Knot Theory, a topic that resonated with me thanks to my childhood spent learning survival skills with my church community. We frequently used knots to build tents, ladders, and stretchers, and I was always fascinated by how tension allowed these knots to carry heavy loads. That hands-on experience made learning knot theory, specifically mathematical knots, especially satisfying. I also appreciated the chance to collaborate with my groupmates. We brought unique ideas to our discussions, shared responsibilities, and worked well together, making the project a rewarding learning experience.

Though my early exposure to knots made recognizing and replicating them easy, I realized when demonstrating them to others that the process could be challenging. This prompted me to think: How can I teach knots more efficiently and accessibly? What other ways could I model them? These questions extend beyond knots—3D geometry, graphs, and charts can also be difficult to grasp if presented in only one way. Offering multiple means of representation, such as through text, visuals, and hands-on activities, is essential for any subject. This inspired me to think about applying similar ideas to a math-music project. There are fascinating parallels between math and music - symmetry, patterns, scales, rhythms, etc. Exploring this connection through a project that investigates math and music in different cultures would be an exciting way to highlight math’s universality. 

Link to presentation slides: https://docs.google.com/presentation/d/1wYTgETin8K9mm2xTXP2MH_n5jskdQLL1ENTD1sR11NU/edit?usp=sharing