Irrationality Measure Of $\pi^2$

TL;DR

This paper offers a straightforward proof that the irrationality measure of π² is exactly 2, improving understanding of its approximation properties.

Contribution

It provides a simple proof establishing the irrationality measure of π² as 2, clarifying its approximation characteristics.

Findings

Irrationality measure of π² is exactly 2

Current upper bound estimate is approximately 5.0954

Proof simplifies previous understanding of π²'s irrationality

Abstract

The note provides a simple proof of the irrationality measure $\mu(\pi^2)=2$ of the real number $\pi^2$. The current estimate gives the upper bound $\mu(\pi^2)\leq 5.0954 \ldots$.