We’ve been enjoying going through Kelsey Houstin-Edwards’s new video series. This week’s was a bit more advanced than some of the prior ones, but I gave it a shot with the kids anyway. I tried to focus on connecting the ideas about singularities in the video with some of the 3D printed shapes we’ve been studying from Henry Segerman’s new book.

Also, I’m just getting over a few days with the norovirus, so sorry if this one (including the write up) has a bit less energy than usual.

Here’s the latest PBS Infinite Series video:

Here’s what the boys took away from the video:

Next we looked at a couple of the shapes that Henry Segerman has made to study with shadows. We were able to see (eventually) that the shadow of the north pole would be a point at infinity – or a singularity.

At the end of this video we started looking at a torus, and the conversation took a very interesting topological turn.

So, we landed on a question of what different shapes might be a torus. It took a bit of time to straighten out this idea, but after a few minutes we came to an agreement on what a torus was.

After that we saw that we didn’t have the same singularity problem trying to create a map that we had on the sphere.

After talking about the torus we spent the rest of this video talking about the pseudosphere which has more than one singularity.

So, another great video from Kelsey Houston-Edwards. It was fun connecting her ideas with some of the 3d prints we’ve been studying lately.