# Looking at Dave Richeson’s “Euler’s Gem” book with kids

I stumbled on this book at Barnes & Noble last week:

It is such a delightful read that I thought the kids might enjoy it, too, so I had them read the introduction (~10 pages).

Here’s what they learned:

Next we tried to calculate Euler’s formula for two simple shapes – a tetrahedron and a cube:

After that introduction we moved on to some slightly more complicated shapes – an icosahedron and a rhombic dodecahedron. The rhombic dodecahedron gave the kids a tiny bit of trouble since it doesn’t have quite the same set of symmetries as any of the Platonic solids:

Now we tried two very difficult shapes:

We studied these shapes last week in a couple of projects inspired by an Alexander Bogomolny tweet:

Working through an Alexander Bogomolny probability problem with kids

Connecting yesterday’s probability project with a few old 3d geometry projects

I suspected that this part would be difficult, so I had them count the faces, edges, and verticies of the two shapes off camera. Here’s what they found:

So, since the boys couldn’t agree on the number of verticies, edges, and faces of one of the shapes, I had them build it using our Zometool set to see what was going on. The Zometool set helped, thankfully. Here’s what they found after building the shape (and we got a little help from one of our cats):

Definitely a fun project. It was especially cool to hear the kids realize that the shape they were having difficulty with was (somehow) a torus. Or, as my older son said: “In the torus class of shapes.” I’m excited to try to turn a few other ideas from Richeson’s book into projects for kids.