Sharing Kelsey Houston-Edwards’s video with kids

I saw this amazing video from Kelsey Houston-Edwards yesterday:

I wrote a bit about it last night because I was so excited about it:

An amazing new set of math videos from Kelsey Houston-Edwards

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!

An amazing new set of math videos from Kelsey Houston-Edwards

I happened to see this old tweet from Steven Strogatz today:

Here’s a direct link to the video:

I was super excited to see this new work from Kelsey Houston-Edwards since, for one(!), I was really hoping that mathematicians would publicize the sphere packing result and find ways to make it accessible to the general public:

A challenge for professional mathematicians

I was fortunate to be able to attend Maryna Viazovska’s talk at Harvard and Henry Cohn’s talk about BU about the new sphere packing results. Although I don’t have nearly the mathematical sophistication to be able to write about the result in any detail, both talks were great. There’s also a link in the post below to a nice talk from Henry Cohn about the history of the sphere packing problem, but I think that’s as close as you can get to the problem without diving into very heavy math:

Maryna Viazovska’s Sphere Packing talk at Harvard

Because of the difficulty of the problem I haven’t been able to figure out to much to do with kids – but I did try two projects in 2 dimensions:

The 2-dimensional version of the sphere packing problem is a fun problem to explore with kids:

Sphere packing – well . . . Circle packing with kids

Using a Natalie Wolchover article to talk about hyperuniform distributions kids

The two higher dimensional sphere problems that Houston-Edwards discusses in the 2nd part of the video are ideas that are accessible to kids.

An old tweet from Steven Strogatz had inspired me to try to talk to kids about the area and volume of circles in different dimensions:

Showing the kids about the area of a circle

We’ll try a new project tomorrow to understand some of the volume properties mention in Houston-Edwards’s video.

I learned the problem about the central spheres from Bjorn Poonen earlier this year and wrote about it here:

A Strange Problem I overheard Bjorn Poonen discussing

Bjorn Poonen’s n-dimensional sphere problem with kids

A fun surprise in Bjorn Poonen’s n-dimensional sphere problem

I called the problem “Bjorn Poonen’s n-dimensional sphere problem” because I learned about it from him. So, to be 100% clear, he wasn’t taking credit for the problem. I learned later from Alexander Bogomolny that at least the two parts of the problem discussed in the video were attributed to Leo Moser

I don’t know the origin of the 3rd part of Poonen’s problem.

The “fun surprise” in the last post discusses an unexpected relationship between \pi and $\latex e$ that makes the 3rd part of Poonen’s problem work.

Anyway, I’m really excited for this new video series – can’t wait to see what comes next!