A Good Day in the Classroom

Today I had planned to spend 50 minutes on the Pinwheel Tiling.

It takes way more planning to spend 50 minutes on too little material than it does to spend 50 minutes on too much material. Doing too much is easy -- you just talk faster. Having too little is much harder, as coming up with things to fill the time takes more skill. And more time planning. At least for me.

So today's class involved a recap of symmetry, and then I talked about various types of tilings and showed some pictures. We looked at pictures of quilts. We looked at pictures of Islamic art. I talked about how you can make fairly precise descriptions of what makes a pattern look "Islamic" versus "patchwork quilt." We saw the Penrose Tiles. And I told them about the toilet paper lawsuit. And then I introduced the Pinwheel tiling. I reminded them that they had seen John H. Conway in The Proof. They asked if I'd ever met him. (I have!) They asked what he's like. I told them. I told them what mathematicians are like.

And then finally I had them cut triangles out of paper and make a super-super-tile of the pinwheel pattern. During which time we also informally talked about advising and how if you're going to take Spanish at community college that you need to do it before you reach your last 30 hours because you can't transfer any courses in during your last 30 hours. And once we were done with making our model of the tiling, we used those weird spiky clippy things that are used for clipping things to the walls of fabric-panel cubicles and stuck the model to the fabric-coated echo-preventing padding that covers the walls of my classroom. (Yes, I teach in a padded room.)

At the end of the class the art major told me that he was thinking of using this tiling in a project he's working on for one of his art classes.

Now I have set the bar fairly high and will need to figure out how to make the Platonic Solids interesting on Friday.