Consider a scenario where a big block collide in a purely elastic way with a small block on a frictionless surface against a wall. If we count the number of collisions of the small block, it will be equal to the digits of π. If we increase the mass of the big block, our estimation of the number of collisions will become more accurate.
To calculate π we use momentum and energy conservation, as well as phase diagram analysis. A more detailed explanation of this can be found on the 3Blue1Brown website.