Exploring n-dimensional cubes with my younger son

During break I’m going to try to do a fun exploration of n-dimensional cubes and spheres with my younger son. Today we talked a bit about cubes and started with by discussing what a “cube” was in a few different dimensions:

Next we talked about a different way to define a cube in n-dimensions using coordinates. These coordinates will help us do a few calculations in the next video.

We wrapped up today by trying to figure out what the longest distance between two points was in a 4-dimensional cube (with side length 1). My son talking through this problem is a really nice example of how kids can grapple with pretty abstract problems: