Sobre o método da exaustão de eudoxo e o cálculo de áreas de regiões planas

Abstract

This dissertation proposes to work the area's concept flat regions such a that of a parabolic segment and on the a power function's grph with rational exponent from techniques and knowledge developed by ancient mathematicians, such as the Exhaustion Method's Eudoxus and the ideas of Archemedes and Fermat, which are not addressed in current school curriculum. This proposal aims to provide a way to work in the basic education themes mentioned here, taking advantage of the mathematical knowledge available to students at this level. At the end of chapter three we present a way to approach the area's calculation of a parabolic segment from concepts of quadratic function, cartesian plan, determinants, modulus, etc. At the end of chapter four we propose an activity for calculating the area of a region on the a power function's graph.