A note on the isoperimetric inequality in the plane

TL;DR

This paper presents a new proof of the classical isoperimetric inequality in the plane, demonstrating that the circle maximizes enclosed area for a given perimeter, using ideas inspired by Demar.

Contribution

The paper introduces a novel proof technique for the isoperimetric inequality based on ideas from Demar, offering an alternative perspective.

Findings

Reaffirms the circle's optimality in the isoperimetric problem

Provides a new proof approach inspired by Demar's ideas

Enhances understanding of geometric inequalities

Abstract

It is well known that among all closed bounded curves in the plane with the given perimeter, the circle encloses the maximum area. There are many proofs in the literature. In this article we have given a new proof using some ideas of Demar.