Watch π emerge from pure chance: random points rain on a square with a circle inside, and the ratio that lands in the circle is exactly π/4. No formula — just probability converging on a universal constant.
The area of the circle is πr² and the square around it is (2r)², so the circle covers π/4 of the square. If points fall uniformly at random, the fraction inside the circle tends to π/4 — so 4 × that fraction tends to π. You're measuring π without ever using a circle formula, just the law of large numbers.