Ever wonder how mathematicians know Pi to so many decimal places? Turns out there's a series to calculate it: 4/1 - 4/3 + 4/5 - 4/7 ...
Here's a program I wrote to illustrate how the series converges on Pi: Calculating Pi Using a Series
Here's another program I wrote to show how Pi can be approximated by randomly placing dots on a square and seeing how many fall within a circle: Random way to Calculate Pi
A short program to demonstrate recursion: Simple Recursion Example