# Throwing $\pi$ at a wall

## TL;DR

This paper presents a method to approximate pi by counting elastic collisions between two masses and a wall, where the number of collisions encodes the digits of pi, linking physics to mathematical constants.

## Contribution

It introduces a novel physical simulation approach to calculate pi using elastic collisions, connecting classical mechanics with number theory.

## Key findings

- Number of collisions equals the first d digits of pi
- Method accurately encodes pi in collision counts
- Applicable for integer values of d in the collision model

## Abstract

We discuss a method for calculating $ \pi $ using elastic collision between two masses $ M $ and $ m $, with $ X = m/M = 10^{2(1-d)} $ where $ d $ is an integer, and a wall. The total number of collisions between $ M $, $ m $ and the wall corresponds to the first $ d $ digits of $ \pi $.