Dynamic geometry and the rebuilding of the Greek geometric thought in the classroom

Abstract

The use of dynamic geometry softwares by the students in the Mathematics class¬es, based in historical and philosophical principles, can bring back a geometric thought that, according to the Greeks, would lead to the world of knowledge. This historical path, exemplified with some constructions made by Apollonius and Archimedes using the means of dynamic geometry with Cabri Géomètre II, will be the point of this study to verify the proposed hypotheses. Thus we are going to prove in real time the definition of parabola through the areas made by Apollonius and the Archimedes’ prove of the sum of the triangles areas obtained from a parabola segment limited by a parabolic arc.