Notions about the nature of Geometry

Abstract

In this paper we discuss, from a historical and philosophical point of view, a variation of the meaning of the five postulates in Euclidean Geometry and we make a short reference to D. Hilberts formalism. We examine, throughout the ages, the question what is Geometry by studying the segmentation and the unification of various geometries, been introduced by F. Kleins Erlangen Program. We concisely present three out of nine Cayley-Klein geometries and then we conclude with some didactic perspectives.