## Dave Radcliffe’s polynomial activity day 1

Saw this really fun tweet from Dave Radcliffe yesterday:

This looked like a fun project for kids, though it wasn’t obvious how to get started. It turns out that Mathematica has a handy function called PolynomialMod[] that tells you what a polynomial looks like modulo an integer – so that made life easier!

I decided that for today’s project we’d explore $(1 + x)^n$ using Mathematica and see what patterns we could find. The introduction to today’s project involved introducing basic polynomial multiplication. Luckily, a natural way to multiply polynomials looks a lot like multiplying 2-digit numbers. I used that connection to introduce the project:

After the introduction I had the boys play on Mathematica and compute various powers of $(1 + x)^n$ starting with $(1 + x)^0$. We got a little confused between Fibonacci numbers and Pascal’s triangle, but here is what they saw:

For the last part of the project today we used PolynomialMod[] to look at the various powers of $(1 + x)^n$ in mod 2. I wanted to get them used to this Mathematica function to make it easier to explore $(1 + x + x^2)^n$ mod 2 tomorrow. After they explored the powers of $(1 + x)^n$ mod 2 up to n = 8, we talked about patterns in the numbers:

So, a fun little computer math project. It was fun to hear the kids talk about the patterns and also fun to talk about some basic ideas like polynomial multiplication and modular arithmetic. Definitely excited to explore some of the more complicated patters tomorrow.