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Preserved in Portico This version is not peer-reviewed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. https://doi.org/10.20944/preprints202106.0636.v1 Giménez, J.; Thaqi, X.; Vanegas, Y. Geometrical Transformations and Development of Geometry. Preprints 2021, 2021060636. https://doi.org/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
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment