Yesterday I learned about the Arctic Circle theorem and used it for a fun talk with the kids:

The Arctic Circle Theorem

This morning we had a fun little coincidence as one of the problems that my son was working on was the proof that . The coincidence is that the number of different tilings of the nth Aztec Diamond is , so for a quick project this morning we looked at the sum and then tried to find the 8 different tilings of the level 2 Aztec Diamond:

Part 1 is a short discussion of the sum:

Part 2 is looking at the tilings of the Aztec Diamond – counting the number of tilings of the level 2 diamond is a pretty good challenge for kids.

So, a lucky second project with the Aztec Diamond. I definitely want to think more about how to share the ideas in the Arctic circle theorem with kids. I think the ideas here are something that kids will really love.

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There are other fun problems about counting tilings. The first one I’d give them is counting domino tilings of a 2-by-n rectangle. Then rhombus tilings of an equiangular hexagon with sides of length a,b,1,a,b,1. If the kids like these, let me know; I can suggest some fun follow-ups.

On the T heading back home from Cambridge. the 2 by n tiling just made me smile. Hope to try it out this weekend. Thanks.