Successive approximations of $\pi$ using Euler Beta functions

TL;DR

This paper presents a didactic method for deriving successive approximations of π using Euler Beta functions, involving polynomial roots, integrals, and inequalities, suitable for undergraduate education.

Contribution

It introduces a novel educational approach to approximate π through Euler Beta functions, combining various mathematical concepts in a didactic manner.

Findings

Successful derivation of successive π approximations

Educational value for undergraduate learning

Integration of polynomial roots, integrals, and inequalities

Abstract

In this didactic note, we describe a procedure to derive successive approximations of $\pi$ using Euler Beta functions. It is an interesting exercise for undergraduate students, since it involves polynomial roots, integral calculations, inequalities and Euler Beta functions.