Grant Sanderson’s latest video explaining a connection between pi and prime numbers is absolutely fantastic:

This video is sort of at the edge of what kids can understand, but it was fun to explore a few of the ideas with them even if understanding 100% of the video was probably not realistic. Our project on the first 10 min of the video is here:

I intended to divide our study of Sanderson’s video into three 10 minute sections, but the second 20 minutes was so compelling that we just watched it all the way through. After watching the last 20 min a 2nd time this morning I asked the kids what they found interesting. The three topics that they brought up were:

(i) The function,

(ii) The formula for , and

(iii) Factoring ideas in the Gaussian integers

Following the introduction, we talked about the three topics. The first was factoring in the Gaussian integers. We talked about this topic in yesterday’s project, too.

Next we talked about the function. I had no idea how the discussion here was going to go, actually, but it turned out to be fantastic. The boys thought the function looked a lot like “remainder mod 4”. Why it does look like that and why it doesn’t look like that is a really neat conversation with kids.

Finally we talked through the formula that Sanderson explained for It probably goes without saying that Sanderson’s explanation is better than what we did here, but it was nice to hear what the boys remembered from seeing Sanderson’s video twice.

I love having the opportunity to share advanced math with kids. I don’t really have any background in number theory and probably wouldn’t have tackled this project with out Sanderson’s video to show me the path forward. It really is amazing what resources are on line these days!