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.

Advertisements

Comments

2 Comments so far. Leave a comment below.
  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.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: