They were laughing and playing Tic-Tac-Toe. At 7:45am, no less. So I wandered into the math center to see just what was so exciting to the handful of math majors gathered around the computer before their Algebra class.

It turns out they were playing Tic Tac Toe on a Klein Bottle. Several of our students went to the Hudson River Undergraduate Mathematics Conference this past weekend, and the keynote speaker, Jeff Weeks (a freelance mathematician) had presented several geometry games. The students were playing Torus Games, in which traditional games like tic tac toe or billiards are played on a torus or on a Klein bottle. And I was jealous, because suddenly Tic Tac Toe looked like fun, so I downloaded the software myself and played a game. Here’s a screenshot of me having beat the computer on the Klein Bottle:

*Screenshot posted with permission*

Because it’s a Klein bottle, when you move down to the bottom it’s the same as moving up, but with left and right switched; the sides are likewise connected, although you stay in the same row. You can even hold down the cursor and move the board around to see how it behaves like an infinite board. It reminded me a little bit of Möbius Chess.

There’s a bunch of other free stuff, too, at Jeff’s main site of Topology and Geometry Software, like Kali for making wallpaper pattern designs and the 3d Kaleido Tile. (I had a lot of fun moving the center point and seeing solids morph into other solids.)

Meanwhile, the students had moved on to exploring the shape of the universe. Not too bad for a Monday morning.