Talking about the Gaussian Integers with my younger son

My younger son is reading The Book of Numbers by Conway and Guy right now:

1/5 The project that I'm doing with my younger son today comes from a really happy coincidence with a few math ideas I've seen online in the last couple of weeks. He's currently reading Conway and Guy's The Book of Numbers and the binomial theorem caught his attention pic.twitter.com/dolyPeNin5

— Mike Lawler (@mikeandallie) February 27, 2021

Last night he read about the Gaussian and Eisenstein Integers. Today we talked about the them (well, just Guassian integers).

Here’s the introduction to what they are in his words:

Before diving into the Gaussian integers, I asked him to give some of the ideas he thought were important in the regular integers. The talk here gave us some good things to talk about in the next video:

Now we talked about Gaussian integers – one fun thing he talked about here was that multiplication by i was the same as rotating by 90 degrees:

To wrap up today’s project we talked about why the number 5 is not a prime in the Gaussian integers. It was nice that he was able to show this!

I’m excited to introduce the Eisenstein integers tomorrow – hopefully today’s project helps prepare for the slightly more complicated math we’ll see there.