π Day programming activity

In our math club this afternoon, since it’s π day, I’m going to try to lead an activity where we write a program (on the Raspberry Pi, of course) that computes π. The idea I thought of (but we’ll see what the students think of as well) is to use the Monte Carlo method – guess random points (with uniform distribution) in a 2r x 2r square, and compute whether they’re “inCircle” or not (whether the distance from the center of the square <= r). Then use algebra to solve for the unknown quantity π in the formula

π r² / 4r² = inCircle / totalPoints

In my little Python program that does this, it pretty quickly gets to 3.14, but doesn’t get much further. Since these are 4th – 8th graders, I thought I should focus on techniques that have an intuition behind them, so Ramanujan’s fancy equations are out of the question. I’d be keen to hear other suggestions!