A contribuição da geometria hiperbólica na formação dos professores de matemática

Abstract

This paper addresses hyperbolic geometry as a conceptual and pedagogical alternative to traditional Euclidean geometry, with an emphasis on its relevance for the training of mathematics teachers. Hyperbolic geometry, characterized by a space of negative curvature and the negation of Euclid's postulate of parallel lines, offers a new perspective on the concepts of straight line, angle and distance. The research investigates the contributions of this geometry to teacher training, highlighting its potential to develop critical thinking and logical reasoning in future teachers. Models such as the Poincaré disk and the Klein plane are presented as effective teaching tools for the visualization and teaching of hyperbolic concepts, especially when integrated with technological resources such as Geogebra software. Despite the didactic and conceptual challenges related to its complexity and the scarcity of accessible materials, the inclusion of hyperbolic geometry in the mathematics undergraduate curriculum can enrich teacher training, promoting a more flexible and creative approach to teaching mathematics.