The Irrationality Measure of Pi is at most 7.103205334137...

TL;DR

This paper improves the upper bound on the irrationality measure of pi from approximately 7.6063 to 7.1032 using a variant of Salikhov's proof, supported by a Maple computational package.

Contribution

It presents a new, more precise upper bound on pi's irrationality measure, refining prior results with a rigorous proof and computational tools.

Findings

Irrationality measure of pi is at most 7.1032

The proof is based on a variant of Salikhov's method

A Maple package supports the proof

Abstract

We use a variant of Salikhov's ingenious proof that the irrationality measure of $\pi$ is at most $7.606308\dots$ to prove that, in fact, it is at most $7.103205334137\dots$. Accompanying Maple package: While this article has a fully rigorous human-made and human-readable proof of the claim in the title, it was discovered thanks to the Maple package available from http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/pimeas.html