On Non-Euclidean Geometry
Non-Euclidean Geometry, Fifth Postulate of Euclid, Educational Softwares.
In this work we present an introductory text of the non-Euclidean geometries focusing on the study of the differences with Euclidean geometry, approaching all the development of the same and its main exponents. Euclid of Alexandria is considered the father of geometry, thanks to his ability to write and expose geometric concepts, being the first to use rigor in mathematical demonstrations. We discuss the emergence of non-Euclidean geometries with the study of the fifth postulate of Euclid, the only one of the five that was unclear about its validity. Next, we show two educational software of dynamic geometry, Cinderella and Geogebra, used to facilitate the understanding about the models that we use in non-Euclidean geometry. Finally, we propose activities for teachers and students that will allow the appropriation of the concepts of these geometries.