||Exploring loci of points by DGS and CAS in teaching geometry
||Jakub JAREŠ and Pavel PECH
The article is aimed at searching for loci of points of given properties using dynamic geometry systems (DGS) and computer algebra systems (CAS) in teaching geometry. Loci of points belong to difficult topics of school curricula at all levels of mathematics education. New technologies can facilitate these topics. By DGS we demonstrate a problem. DGS also enables us to find the searched locus and state a conjecture. To identify the locus equation we use CAS which perform symbolic computations. In addition, in those cases, where it is possible, a classical proof is given as well. This method is demonstrated in several examples from 2D and 3D geometry.