The earliest records of pi date back to 2000 BCE from the Babylonians, who estimated pi to be 3.125. They, along with ancient Egyptians, recognized that pi was a constant ratio that is true for any circle. The famous mathematician Archimedes made better approximations by inscribing and circumscribing a circle with polygons of an increasing number of sides. By increasing the number of sides, further digits of pi can be obtained, since a circle is a shape with infinite sides. However, this method is extremely tedious and complicated, making it difficult to calculate more digits of pi.

But why do we even need so many digits of pi? The Jet Propulsion Laboratory of NASA uses 3.141592653589793 for pi in their highest accuracy calculations. If we consider the largest circle we can conceive of - the universe, which has a radius of 46 billion light years -  only 38 digits of pi are needed to achieve an accuracy of the diameter of a hydrogen atom. Rather than calculations for physical space, computing pi has become a benchmark test for computers. Calculating such a large number of digits of pi is a real challenge that requires a lot of computing power. However, it is also verifiable, which means that we can find out if the hardware and software of a computer perform correctly. 

An interesting example of calculating pi appears in colliding objects. In stark contrast to the formulae above, this way of finding pi is entirely deterministic and incredibly simple. By “colliding” in a dynamical system of two billiard balls and a perfectly inelastic object, assuming zero friction, air resistance, and perfectly elastic collisions, we can find pi by counting the collisions. "To obtain an accuracy of N decimal digits, one needs just to take the balls with the appropriate masses: the ratio of the masses should be chosen to be the N th power of 100 (Galperin, 2003)." For example, a 1kg block (block A) heading towards a wall collides with another 1kg block (block B) in front of the wall. In a perfectly elastic collision, they exchange velocities, causing block B to collide with the wall and bounce back, keeping the speed but changing direction. Block B has a perfectly elastic collision with block A, making three collisions in total. If we increase the mass of block A to 100kg, it retains most of its inertia during the collision with block B. The number of collisions increases to 31. By continuing this cycle - 314, 31415, 314159…, we find pi.