Ensinando geometria não euclidiana na educação básica: uma proposta relacionando as geometrias esférica e hiperbólica

Abstract

In this work we present a spherical and hyperbolic geometries teaching approach for the secondary education, in which the software Geogebra is used. This study is developed from the geometries of the spherical and hyperbolic spaces, its projections and symmetries. In addition, the non-Euclidean models can be naturally obtained from the hyperbolic space projections in the plane, which is inspired by the Beltrami’s ideas in the creation of these models. These projections are similar to different map projections. Therefore, there is a conection between these geometries, which contributes for the learning process of such concepts. The study of the projections also allows, in a natural way, the students to make a piece of art using “hyperbolic” tilings which can have a visual appeal.