Math Art Project Write Up

Original Artwork By Holly Laws

Tricolorability of Trefoil Knot

 

Our group's rendition of Trefoil Knot made with clay

 

Our group - Jasmine, 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. 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.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.

It was really fascinating to discover the major real life applications knot theory had in scientific research. It was during this process that I found out that the basis of research for understanding Alzheimers was knot theory! I will definitely be doing a lot more research on this. The frustrating part with this project for me was that there were not any applications of this that coincided with the high school BC math curriculum. 

While I found this project to be a fun activity that would interest students to further research this topic, I do not think I would be able to indulge in this as a teacher if covering the core competencies and big ideas is to be given priority. However, working on this project and seeing my classmates present their art projects, I learned that projects like this one can be done just for the sake of art and connecting a few dots with mathematics. In my future classroom, perhaps math art projects can be a little break from "harder" topics.

Here is the link to the slides: https://docs.google.com/presentation/d/1wYTgETin8K9mm2xTXP2MH_n5jskdQLL1ENTD1sR11NU/edit?usp=sharing