Caculate Pi using a physics simulation of elastic collisions https://www.youtube.com/watch?v=HEfHFsfGXjs

bouncy_pi.py

#!/usr/bin/python3
import math

DIGITS = 4

class Body:

    def __init__(self, pos, vel, mass):
        self.pos = float(pos)
        self.vel = float(vel)
        self.mass = float(mass)

    def advance(self, time):
        self.pos += self.vel * time

    def get_velocity_after_collision_with(self, body):
        if self.mass == math.inf:
            return self.vel
        if body.mass == math.inf:
            return -self.vel
        return ((self.mass * self.vel + body.mass * (2 * body.vel - self.vel))
                / (self.mass + body.mass))

    def __str__(self):
        return "pos={:.3f};vel={:.3f};mass={:.1f}".format(
                self.pos, self.vel, self.mass)

a = Body(1, 0, 1)
b = Body(2, -1, 100**DIGITS)
wall = Body(0, 0, math.inf)

def time_until_collision(left_body, right_body):
    vel_diff = left_body.vel - right_body.vel
    if vel_diff > 0: # bodies moving towards each other
        return (right_body.pos - left_body.pos) / vel_diff
    return math.inf

def update_velocity_after_collision(body1, body2):
    vel1 = body1.get_velocity_after_collision_with(body2)
    vel2 = body2.get_velocity_after_collision_with(body1)
    body1.vel = vel1
    body2.vel = vel2

total_time = 0
total_collisions = 0

while True:
    time_wall_a = time_until_collision(wall, a)
    time_a_b = time_until_collision(a, b)
    if time_wall_a == math.inf and time_a_b == math.inf:
        break
    if time_a_b < time_wall_a:
        col_type = "a-b" # collision between body a and b happens next
        time = time_a_b
    else:
        col_type = "w-a" # collision between wall and body a happens next
        time = time_wall_a
    total_time += time
    total_collisions += 1
    a.advance(time)
    b.advance(time)
    wall.advance(time)
    if col_type == "a-b":
        update_velocity_after_collision(a, b)
    elif col_type == "w-a":
        update_velocity_after_collision(wall, a)
    if DIGITS <= 4:
        print("{} num={} time={:.3f} a({}) b({}) w({})".format(
            col_type, total_collisions, total_time, a, b, wall))

print("Pi is {}".format(total_collisions/10**DIGITS))