Yesterday we watched this fantastic video by Mathologer on Fermat’s Two Squares theorem:

I’m hoping that we can do a couple of different projects based on the video. Today we talked about some ideas from the video and wrote a project to explore sums of squares.

We began by discussing some of the ideas in the video that the boys found interesting, and then talked through a few of the proof ideas from the vdeo:

Next we checked out one of the algebraic identities that came up in the Mathologer video. I thought that checking these identities would be good algebra practice.

Finally, we went to Mathematica to write a program to look at sums of squares. There was one slightly tricky part of the program that took a minute or two for the boys to explain. I thought that they had understood this concept while we were writing the program, so it turned out to be sort of lucky that we went back to talk about it.

Anyway, here’s the program that we wrote and a little bit of play with the numbers. The surprise was that it seemed like almost all of the numbers that could be written as sums of squares in lots of ways were multiples of 5. We might explore this idea a bit more in a later project.

Fermat’s Two Squares is really fun to explore with kids – and Mathologer’s video is a great way to show kids an proof that they can understand. I’m excited to explore the ideas a bit more with the boys later this week.