A historical and epistemological study on the mathematical object Orthogonal Symmetry

Abstract

This work is an excerpt from an already completed doctoral thesis, in which we conducted a study on the mathematical object Geometric Transformations in the plane, more specifically on Orthogonal Symmetry. Initially, we present some elements of the historical and epistemological development of Geometric Transformations in the plane, followed by the importance of the group of geometric transformations in the classification of geometries and, finally, a study on orthogonal symmetry. The aim of this study was to understand the mathematical object Orthogonal Symmetry from both a historical and epistemological point of view, for this, it was necessary to cover a larger field of knowledge. The article favors the understanding of the importance of teachers and future mathematics teachers to understand Orthogonal Symmetry not only as symmetry in the object, in which the role of the axis of symmetry in geometric figures, its characteristics in elements of nature and its influence in the art world, but also the mathematical object Orthogonal Symmetry in which its definition and mathematical properties must be studied.