Buffon's Triangle -- A Variant of the Buffon Needle Method for a Probabilistic Determination of the Value of Pi

TL;DR

This paper introduces a novel variant of Buffon's Needle method that uses random equilateral triangle casting onto a tiled floor to probabilistically estimate pi, with accompanying source code for simulation.

Contribution

It presents a new geometric approach to estimate pi using triangles instead of needles, expanding Buffon's method with a different shape and floor configuration.

Findings

Successfully estimates pi through simulation

Provides source code for reproducibility

Demonstrates the method's potential accuracy

Abstract

I present a variant of the Buffon Needle method for determination of the value of the mathematical constant, pi. The original method is based on the random casting of a needle of length l onto a planked floor of plank width L. The described variant involves the random casting of an equilateral triangle with side length l onto a tiled floor consisting of square tiles of side width L. Source code for the computer simulation of this method is provided.