Typically, I haven’t liked celebrating Pi Day. Interrupting learning just to eat pie or recite memorized digits just seems like a waste of everyone’s time. But these are the things that students and popular culture associate with Pi Day celebrations. Today is different, though. Today, I have the chance to weave learning into Pi Day.
It’s the last week of the term, so my 3D geometry students are working on final projects. I don’t feel too badly interrupting them to have them wonder a bit about the weirdness of pi. There are lots of ideas about this in James Tanton’s Weird Ways to Work with Pi, which I was happy to find. I was wondering what “pi” would look like for regular polygons like a triangle, or a square, or an octagon. Could we even talk about pi for polygons? And then I happened upon Tanton’s book. So today, I’m asking my geometry students to consider the question, “What does pi look like for regular polygons?”
I also have a class called “Social Decision Making.” It’s about voting methods, fair division, and a bit of game theory. So, in the only class where sharing a pie among 10 people is a relevant mathematical activity, we’re going to divide a pie, fairly, for all of us. Depending on the number of students in class, we might even just use parallel cuts, to make it interesting.