New methods of Classical Loci Determination

Aim of this paper is to rediscover well known geometric loci through constructions that are new and completely different from the ones originally introduced by those mathematicians who first studied their properties. The methods presented allow to observe the genesis of the considered loci from a viewpoint which agrees with the intuitive dynamic image of a geometric locus, as a point moving in the plane according to its links with other points. Several examples are included, to show that geometric loci may be obtained not only by constructive methods, but also through new procedures that highlight the loci intrinsic beauty. A computer algebra method is implemented to automate the proposed new derivation of the old loci.