# Why I love sharing ideas from research mathematicians with my kids

Yesterday we did a project inspired by the great podcast conversation between Steven Strogatz and Federico Ardila here:

That project is here:

https://mikesmathpage.wordpress.com/2021/04/03/revisiting-the-permutahedron-with-my-younger-son-after-listening-to-steven-strogatzs-interview-with-federico-ardila/

Last night I asked my younger son what he wanted to do today for a project and he said that he wanted to talk about the permutahedron a bit more. In yesterday’s project we talked about the permutations of the set (1, 2, 3, 4), so today we started by going down to some simpler sets of permutations:

Next we looked at the shape made by the permutations of the set (1, 2, 3). The way my son thinks through this problem shows why I love sharing ideas from math research to my kids.

To wrap up today we dove a little deeper into one of the ideas we talked about yesterday – in the permutations of the set (1, 2, 3, 4) is there a permutation that requires 4 or more flips to get back to the starting point of (1, 2, 3, 4)?

The permutahedron is a really neat shape to explore with kids, and hearing them talk about and think through the shape itself is incredibly fun.