Preprint Communication Version 1 Preserved in Portico This version is not peer-reviewed

Geometrical Transformations and Development of Geometry

Version 1 : Received: 25 June 2021 / Approved: 28 June 2021 / Online: 28 June 2021 (10:23:43 CEST)

How to cite: Giménez, J.; Thaqi, X.; Vanegas, Y. Geometrical Transformations and Development of Geometry. Preprints 2021, 2021060636 (doi: 10.20944/preprints202106.0636.v1). Giménez, J.; Thaqi, X.; Vanegas, Y. Geometrical Transformations and Development of Geometry. Preprints 2021, 2021060636 (doi: 10.20944/preprints202106.0636.v1).

Abstract

A way of systematizing different geometries by geometrical transformations is presented by using Klein’s perspective. Symmetry is considered the basic precedent, and different groups of transformations are introduced by using Erlangen program ideas. So, to focus on the importance of geometric transformations, two purposes are shown: first, the classification of geometries is based on the invariants of geometric transformations; and second, the construction of geometry unlike the theory of deduction can be done by means of geometric transformations.

Keywords

geometry; geometrical transformations; symmetry; invariance, perspectivity, Möbius transformations.

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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