This project approximates pi by simulating the motion of two perfectly elastic objects on a frictionless plane. Counting the number of times object 1 touches either object 2 or the screen's left edge yields a surprising approximation of pi! The ratio of the masses of object 1 and object 2 (in powers of 100) determines the number of digits in the pi approximation. Press 1, 2, 3, 4, 5, or 6 to see simulations at ratios of 1 to 100^0, 100^1, 100^2, 100^3, 100^4, and 100^5, yielding 1, 2, 3, 4, 5, or 6 digits of pi, respectively.
This was inspired and informed by Daniel Shiffman's Javascript simulation of the same phenomenon: https://youtu.be/PoW8g67XNxA ...which was in turn inspired by this amazing YouTuber: https://youtu.be/HEfHFsfGXjs I don't pretend to fully understand the math at work here, but the graph up top shows the relationship between the velocities of the two objects. Its circular shape is dictated by the formula for conservation of energy in elastic collisions: m1*v1^2 + m2*v2^2 = a constant (which is essentially the formula for a circle: x^2 + y^2 = a constant). The collisions divide up the circle at regular intervals, which get smaller and smaller as the number of collisions increases.
