La Baguette Math\'emagique

TL;DR

This paper explores a novel extension of Buffon's needle experiment, demonstrating how it can be used to estimate both π and e simultaneously, offering a new perspective on classical probability methods.

Contribution

It introduces a method to estimate both π and e using the same Buffon's needle experiment, which has not been previously discussed in this way.

Findings

Both π and e can be estimated from a single Buffon's needle experiment.

The method provides a new probabilistic approach to fundamental constants.

The approach extends classical geometric probability techniques.

Abstract

If you throw a needle or stick at random onto a floor ruled with parallel lines, such as the cracks between floorboards or tiles, from the proportion of times that the stick lands crossing a crack you can estimate $\pi$; can we get $e$ as well? Yes, we can. All of these aspects have been discussed before, but I haven't seen them discussed in this way: that one can estimate both $\pi$ and $e$ with the same Buffon's needle experiment.