The use of GeoGebra for exploring some constructions of Euclid, Archimedes and Apollonius

This paper describes a mathematical laboratory path designed and tested as part of a university course of History of Mathematics. This laboratory path was developed in collaboration with PopMat1 laboratory of the University of Trento. For carrying out the activities that make up the laboratory, we used the dynamic geometry software GeoGebra2, which, thanks to its characteristics, facilitated the participants in the process of reconstructing the mathematical thought of Euclid, Archimedes and Apollonius. The purely geometric approach to the problems considered with GeoGebra makes it possible to design teaching/learning opportunities in which it is required a drastic change of point of view (compared to the usual one, that is analytical), which we consider particularly stimulating and useful in the training process of future teachers.