I swam at 7 am, in the Knute Rockne Pool. Ate breakfast in the most amazing college dining hall I've ever experienced. And made my way over to our daily meeting place. In prior years, we walked all those calories off getting between far-flung buildings. Not this year. Easy on the feet, hard on the belly.
The Kaplans started us off with this problem: A light ray leaves one side of a mirrored square. What happens. We discussed the physics of it, and tried to get away from that, back to math. We talked about modeling this as a billiard table instead. We kinda sorta proved that angle of incidence = angle of reflection. We never worked together on the question that pulled me: How many line segments will be made by the path of the light, before it gets back to its starting point? I figured something out, but I'm not sure yet why it would be true, so it could be wrong. It was a great problem to pull people in at lots of different levels - I think.
Then we talked about relating math circle stuff to classroom teaching, since most of us attending are teachers. Then lunch.
In the afternoon, the kids came. Bob, Ellen, Tatiana, Anand, Amanda, and Rodi did math circles with the kids, and we all watched. Afterward we discussed what went right and what went wrong. Plans for tomorrow, then dinner.
There's a lounge in our dorm. We met in the lounge, and Bob ran a session on sizes of infinity. Those of us who knew the 'answers' managed to keep our mouths shut. I showed off my manuscript to a few people. It's bedtime, but I wanted to do what Fawn did and offer you some notes, so here they are.