Uma visita ao disco de Poincaré: proposta de material para aperfeiçoamento de professores

Abstract

This work proposes a support material for teaching non-Euclidean geometries, which can be used during initial teacher training or teacher improvement. We will do this by means of a model of the hyperbolic geometry known as the Poincaré disk. This model has great importance in mathematics in part because it allows the visualization of the properties of this geometry. Thus, we expect the support material we produced to facilitate the study and interpretation of such properties, which make hyperbolic geometry so different from Euclidean geometry. The support material devotes an entire chapter to a historical approach to the development of non-Euclidean geometry. Another chapter is devoted to definitions and results of Euclidean geometry, and can be used to revisit these topics, regardless of the interest in the Poincaré disk.