Measure π with random darts
Darts land at random points in a square. A quarter circle sits inside it. The fraction of darts inside the curve tells you the area of the quarter circle, and that gives π. More darts, better estimate, but slowly.
What's going on
The square has side 1, so area 1. The quarter circle has radius 1, so its area is π/4. A random dart lands inside the quarter circle with probability (area inside) ÷ (area of square) = π/4. So four times the fraction inside is an estimate of π.
How does the computer know a dart is inside? By Pythagoras. A dart at (x, y) is at distance √(x² + y²) from the corner. It is inside the circle when x² + y² ≤ 1.
The error shrinks roughly like 1 over the square root of the number of darts. To get one more correct digit you need about 100 times more darts. That is why this is a fun method, not a fast one.
Sheets: Dice don't lie and Pythagoras and square roots.