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

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.