Propriedades intrínsecas de superfícies regulares: explorando geometrias não euclidianas com aplicações didáticas no Ensino Médio

Abstract

In this work, we applied a math lesson plan to a second grade high school class at a public school in the state of Bahia. The students worked on non-Euclidean geometry topics. In developing the lesson plan, we took advantage of the dynamic environment offered by the GeoGebra software and made use of manipulatives. The first stage of the proposal was carried out in the classroom, through questioning we built up the concept of geodesics with the students. The second stage took place in the school’s computer lab, where the students had the opportunity to check the sum of the angles of a triangle in Hyperbolic Geometry and Spherical Geometry models. We also gave a brief summary of the attempts to demonstrate Euclid’s parallel postulate and the emergence of non-Euclidean geometries. In addition, we studied content that is usually covered in a Differential Geometry course, such as regular curves parametrized by arc length, regular surfaces, curvatures and the intrinsic geometry of surfaces. Finally, the students completed a survey in which they recorded their level of satisfaction with learning the following topics: the concept of geodesics, the sum of the internal angles of hyperbolic and spherical triangles, surfaces with positive curvature and surfaces with negative curvature.