Twenty unpublished sphere construction cases modeled with the help of GeoGebra

Abstract

Geometric places are an essential part in solving complex geometric problems, since their own definition represents a way of isolating their possible solutions by applying Euclidean deductive reasoning. One of the fields of application of the most useful three-dimensional geometric places from the didactic point of view is the determination of the center and radius of a sphere. Although these types of problems have gained importance with the origin and emergence of Descriptive Geometry, many of them have been discarded in recent years due to the difficulty of their graphic representation. The emergence of computer programs oriented to dynamic 3D geometry allowed the return to situations whose geometric approaches made their resolution almost impossible in the past. In this communication, twenty unpublished cases of determination of the center and radius of a sphere are presented, as the preliminary review made by the author demonstrates this, whose solutions were found and validated with the support of the GeoGebra software, following a methodology developed and proposed by the author, in order to allow the construction of conjectures, however, without intending to present mathematical tests here.