The second annual Math Fair hosted by the American Institute of Mathematics (AIM) on June 28, 2025 at the California Institute of Technology was truly a delight for all ages and mathematical levels. Just as last year, the attendance topped 700. It was wonderful to see kids build the Platonic Solids — perhaps for the first time in their lives— at the Geometiles table.
This time, I was thrilled to learn new math applications from the participants! The mom of one of the kids was playing around with a chain of 30-60-90 triangles (below) and ended up folding it into a tube. She said it reminded her of origami foldable heart stents (she is an anesthesiologist). This was a revelation for me.
Inspired by her structure, I started playing around with it at home after the festival. In particular, I wanted to see if I could modify the structure so that it connects. This got quite involved and eventually grew into two blogs.
Another concept I learned at the festival was the shape shown below.
One of the participants built this. I had never seen this shape before. The pairs of faces (yellow/yellow, yellow/orange) facing outward look like squares. But are the triangle forming these “squares” truly coplanar? It was time to pack up, so I took this problem home as well. Here are two views of the reconstruction of the same shape.
To rephrase the question, are the yellow “squares” above truly flat squares? Or are they so close to being flat that we cannot detect that they are not. I took this question to a Facebook group on Polyhedra, and it elicited some excellent observations. I am not going to share them here so that you can ponder this yourself!
Events like the AIM Math Fair are a beautiful reminder that math is about curiosity, creativity, and connection. I can’t wait to come back next year!