Math Art Project: Personal Reflection

I had quite a lot of fun working on the artwork! I think we picked a fairly interesting piece and I really enjoyed making polyhedrons out of pipe cleaners. Once I learned the general technique for making square antiprisms, it was quite therapeutic and relaxing to keep making more in the same way that working with yarn or string is. I personally enjoy latch hooking, and I found the process to be somewhat similar to that.

There were lots of interesting mathematical tidbits about the artwork, but we were only able to talk about some of them in our presentation. We were able to highlight the connection of our shape to the platonic solids and how they can be classified by considering how many n-gons fit around each vertex of the shape, and noting that once you get to 6 or 7 triangles you start running out of space. As well, we were able to talk about antiprisms and how they differ from prisms. Our demo ended up taking a while, but had we had more time, we also had more mathematical insights to share. For instance, there's a neat connection between how many shapes you put around a vertex and different types of geometries (spherical, euclidean, and hyperbolic.) We noted that once you reach 7 triangles, you're fitting more than 360 degrees around a point, so you're forced to fold the triangles in both convex and concave ways. This gives the shape some amount of negative curvature (like a "saddle" shape) which mimics the behaviour of hyperbolic geometry. In hyperbolic geometry, space gets "denser" and more "complex" as you move outwards in a way, which provides some intuition as to why there may not exist a polyhedron which has 7 triangles around every one of its vertices. In fact, this is true, and we were able to prove it using Euler's Polyhedral formula (V - E + F = 2) by way of a double-counting argument.

It was nice being able to talk about our artwork in the presentation, but I had some trouble running the demo. People were mostly able to follow along as I walked them through the construction process, but there were several times when I lost confidence and wasn't able to grab the attention of the class. I ended up using the repeat-after-me clapping method to grab people's attention, which worked well, but also felt a bit like fighting volume with volume and made me a little uncomfortable for that reason. I think I probably could've explained the demo a bit more clearly at certain points and with more confidence to keep people more on track. I know that situations like this will arise in the classroom in practicum when walking a class through an activity, so I'll need to try to brainstorm more ways to keep the class's attention. Regardless, I think the demo helped people better understand the overall structure of our artwork and that they enjoyed collaborating on making something together as a class.