# A second example from tiling the Aztec diamond

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 $1 + 2 + 3 + \ldots + n = (n)(n+1) / 2$.  The coincidence is that the number of different tilings of the nth Aztec Diamond is $2^{(n)(n+1)/2}$, 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.

## 2 thoughts on “A second example from tiling the Aztec diamond”

1. 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.

1. 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.