A simple upper bound for the perimeter of an ellipse

TL;DR

This paper presents a straightforward method to derive an upper bound for the perimeter of an ellipse using elliptic integrals, inequalities, and convexity properties, simplifying the calculation process.

Contribution

It introduces a novel, simple derivation technique for bounding an ellipse's perimeter leveraging elliptic integrals and convexity, improving analytical approaches.

Findings

Derived a simple upper bound for ellipse perimeter

Utilized inequalities and convexity properties in the derivation

Provided an analytical calculation method for the bound

Abstract

We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can be calculated analytically.