Statistical approach based on 1D Voronoi tessellation as a tool for studying the randomness of fractional digits of some irrational numbers

TL;DR

This study uses 1D Voronoi tessellation to analyze the randomness of fractional digits of irrational numbers like pi, e, and phi, finding no significant deviations from randomness across millions of digits.

Contribution

It introduces a novel statistical method based on 1D Voronoi tessellation to test the randomness of irrational number digits, validated on large datasets.

Findings

Digits of pi, e, and phi behave as random sequences within numerical error

No detectable difference between irrational digits and random sequences

Method applicable to various irrational numbers with consistent results

Abstract

An "experimental" study on the randomness of the fractional digits of $\pi$, $e$ and $\phi$ irrational numbers are presented. This is done by exploiting the $1D$ Poisson-Voronoi tessellation. We employed two approaches and in both cases, within the numerical error, no differences have been detected between the irrational fractional digits and an equivalent random sequence of digits. The number of tested digits is $1.6 \times 10^7$ and $4 \times 10^7$ for the first and second approach, respectively. Although not shown here, we investigated several irrational numbers and all of them have displayed a similar behavior.