Finishing Dave Radcliffe’s polynomial activity

We’ve spent the last two days talking about a math activity that I saw in a Dave Radcliffe tweet:

Coefficients of (1+x+x^2)^n mod {2,3,4,5}, created using Python and matplotlib. [Correcting previous tweet] pic.twitter.com/fIWuMuTpOi

— David Radcliffe (@daveinstpaul) July 30, 2016

Those two project are here:

Dave Radcliffe’s polynomial activity day 1

Dave Radcliffe’s polynomial activity day 2

My younger son had a few ideas that we didn’t get to finish, so this morning we talked through a few of them. He was exploring (using Mathematica) in mod 3. We started by looking at Radcliffe’s picture:

 

We wrapped up today’s project by trying to find the pattern in the row numbers that had all 1’s for coefficients. This idea was a little bit of a struggle yesterday, but today we did find the pattern:

 

So, a really fun computer math project for kids. It was really fun to use Dave’s pictures to motivate the project and to help the kids explore some of the patterns that they found playing around in Mathematica.