An innovative exhaustion approach for estimating the circumference of a circle and a visualization by Geogebra

Abstract

The method of exhaustion is a technique that Archimedes used to find the area and circumference of the circle or any shape which is bounded by non-linear borders. More generally, the exhaustion technique can be assumed as an earlier form of integral calculus. In this paper first, we will give a modern calculation of Archimedes' own approach to find the circumference of a circle. Additionally, we will propose a new approach and related calculation of the circumference of the circle. We will visualize new approach to calculation of the circumference of a circle by using GeoGebra which is dynamic mathematics software. © IDOSI Publications, 2011.