This week I listened a great conversation between Steven Strogatz and Federico Ardila on the Joy of X podcast:
We have played with the shape a few times before – see these blog posts of you are interested in seeing other ways that kids can explore the shape:
Today we explored the and idea that Ardila discussed in the podcast – finding paths on the permutahedron.
We started by just reviewing what the shape is and what it represents:
Next we tried an easy example of finding a path on the permutahedron going from a random permutation back to the correct order:
For the last part of the project we tried a more complicated scramble of the cards and found that walking back to the unscrambled state would take a minimum of 3 steps:
I love playing with this shape with kids. It is a great way to get them talking about fairly advanced mathematical ideas and also allows them to see a really neat 3d shape that research mathematicians find interesting!