Here’s what my kids thought was neat about the video:

My younger son thought the “central sphere” problem was fun, and my older son thought the shape of the n-dimensional spheres was fun. I originally intended to talk about both this morning, but our talk about the shape of the spheres took enough time for one project.

So, below is our initial look at the shape of the spheres. There’s a lot of nice introductory geometry (and fractions!) in the discussion. Also, I made the choice to talk about 1/2 the length of the long diagonal – that choice sort of confused the kids, so I’d focus on the full length if I was doing this again.

Finally, we talked about how the diagonal changes as you go up in dimension. This is a fairly straightforward application of the Pythagorean theorem, so it isn’t that hard to talk about. The boys saw the pattern fairly quickly.

Then I introduced the volume formula for even-dimensional spheres and we calculated the ratio of the volume of a 30-dimensional sphere to the 30-dimensional box it is inscribed in.

I’m super excited for this new series of videos from Kelsey Houston-Edwards, and I can’t wait to share the next one with my kids!