Arquimedes e o método

Abstract

This paper aims to present two of the most interesting results of the theory developed by Archimedes: the calculation of the area under the parabola - the quadrature of the parabola – and volume of a sphere. Features the famous mechanical method used by him, in fact, uses the law of equilibrium of a lever and, together with the method of exhaustion shows each result with the rigor required at the time. In contrast with the perspective of modern mathematics shows that it is possible to merge the history of mathematics in the teaching calculation of areas of plane geometric figures - in this case, the area bounded by a curve, the parable - and the calculation of the volume of a sphere - using the principle of Cavalieri or even integral calculus – presenting initially empirical and elaborate vision of Archimedes. The purpose of this dissertation aims to provide the math teacher, a new take on the teaching of the history of mathematics topics concurrently with issues traditionally studied in the classroom, enabling the development of differentiated approaches in the teaching these high school subjects.