Here is a way to find π without measuring a single circle: throw darts at a square at random, and count how many land inside a quarter circle drawn in it. Because the quarter circle covers π/4 of the square, four times that share comes out close to π. Throw a few darts, then a million, and see how close you get, and why getting one digit further takes a hundred times as many darts.
This article and its interactive demo were created with the help of generative AI and editorially reviewed.