And now for something completely different

If you're curious what I do in the other half of my professor gig, on Thursday I'm giving an undergrad talk on these:




Puzzles, straightening honeycombs, and adding matrices

Given the three kinds of puzzle pieces pictured above, define a puzzle to be a decomposition of a triangle into puzzle pieces (such that the edges match up, like in a jigsaw puzzle). Call a puzzle ``rigid'' if there is no other puzzle with the same outer boundary. A lot can be proven about puzzles (we'll do (1) and (2) in the talk):

1. The number of 0s on one side equals the number of 0s on each of the other two sides - see if you can prove this one before the talk!

2. The lines in the puzzle pieces can all be simultaneously straightened (as in the right-hand picture) if and only if the puzzle is rigid

3. There is an easy 1:1 correspondence between rigid puzzles and inequalities on the eigenvalues of the sum of two Hermitian matrices

4. The statement ``Given four generic lines in space, there are exactly two others that touch all four,'' and others like it, can be turned into puzzle-counting statements.


Thursday, November 17, 12:00 pm, AP&M 2402
Refreshments provided!