Magic Squares. There is an algorithm for producing a magic square, which is a table of integers whose rows, columns, and diagonals all add up to the same number. Click on the link to see the steps of the algorithm and a large example.

Fractals These are pretty computer generated pictures. Every time I get a new computer I generate some of these just to test how fast the machine is. These are defined by a very simple mathematical algorithm, but it takes a lot of horsepower to generate them. The first time I ever drew one was on my Atari 1040ST. It would take three hours to generate a 320x200x256 colour image. Now I can do the same thing in a couple of seconds!

Here's a little bit of math showing how to compute the number of toothpicks in an order n tetrahedron. I also built the toothpick structures. It's on my woodworking page.