Math Art Projects & Reflection

Submission for the math art project.

Our group connected with Melissa Schumacher's "Counting with Knots" artwork. Melissa's work was creating a celtic knot using numbers from 0 to 26 in base 3. In the first stage of her work, she placed each number (0 0 0, 0 0 1, 0 1 0, etc) on a triangular grid. Each of the numbers corresponded to a specific symbol, which would guide her generation of the pattern. 0 corresponded to a point, 1 to a horizontal barrier, and 2 to a vertical barrier. By stage 2, everything was connected, and in stage 3, she completed the artwork by designating the alternating strands and beautifying the piece. In our group, Allyssa, Jacky, and I each had our own interpretation of Melissa's work by using numbers 0 to 15 in base 4 (0 1 2 3)! Allyssa's work (in the blue & pink) had 3 correspond to an 'X' which meant that the line does not pass in this area. Jacky's work (in the multicolour) had 3 correspond to both a horizontal and vertical barrier-- which interestingly enough did not result in a celtic knot. Finally, my work (in the purple) had 3 correspond to either 2 or 4 strands in the crossing. 

I was really excited about the project, and that perhaps resulted in underestimating the involvement of stage 3. Based on my experience in MATH 308 & MATH 309 (Introduction to knot theory), I didn't have a hard time understanding the mechanics of the knot. The most tense part was re-drawing the grids for stage 3, because stage 3 required an overlay of a hidden stage 2. I needed to resize and transfer the pattern, draw temporary ribbon, appoint alternating strands, fix the ribbon, cross-reference each crossing to stage 2, outline the final ribbon, uncover and track each link, and erase any guides. As involving as it was, I found the slowly-revealing knot very rewarding, and was so happy once it finally turned out! Each of the knots our group created turned out beautifully and deepened my appreciation for the artwork and mathematics of celtic knots. 

In terms of teaching, I firmly believe that if you are committed enough to educating students about a topic, there is always a way to weave it in to your class. This was evident in our presentation, as our group provided multiple teaching ideas for bringing celtic knots into the classroom. This project was wonderful because it showed that mathematics can be very present in artworks which could aid students' interdisciplinary thinking, sequential reasoning, and design skills. The experience encouraged me to think outside the scope of the curriculum, and plant the seeds of seeing mathematics in arts, film, ADST, etc. in students too. Also, upon reflecting on the unanticipated difficulty of our knot activity, some learning activities may require more thought to achieve effective low-floor/high-ceiling points, or require clearer tutorials to evoke more interest and engagement.