Le Curve di Apollonio. Innovazione nei processi risolutivi, il caso della parabola.

Abstract

This study is connected with the research directed on the solving problem of a graphic representation of geometric objects using the informatics language, particularly the graphic software CAD. The solution of these problems requires a reliable command of stereometry and descriptive geometry and it can extend remarkably the level of external geometric competences. The implementation of the means of ICT has brought a higher effectiveness of graphing mapping processes. The modification of informatics means with the goal to simplify applications of descriptive and projective geometry is also of a great didactical importance. In particular, we focus attention on the treatment of the locus "cone", which assumes the character of great generality in the application of the Representation Science. The theoretical and practical study of this curve’s properties could be found since ancient times, outlining, over the centuries, different cultural approaches that trace important aspect of the geometrical/mathematical thought’s evolution. The paper focuses on operational limitations that arise in mathematical modelling software solution to graphics problems of plane geometry and space. In particular, we pay attention on the current digital tools capable of tracing the curves of a second degree in the subject. We present some results of our research aimed to structure new generative algorithms of geometric constructions allowed to represent, in general terms, the famous curves of Apollonius.