Geometria projetiva das cônicas: uma abordagem através do GeoGebra

Abstract

The present work has the general objective of developing pedagogical activities aimed at the teaching and learning of Projective Geometry of Conics in High School, using the GeoGebra software as the main pedagogical tool to explore the properties of Conics through geometric constructions, which favors visualization, critical analysis, and practical application of the basic concepts addressed. Initially, we de ne conics as geometric places, and then we characterize them as plane sections of a cone, using Dandelin Spheres to justify why such curves are called conics. Next, we observe their optical and isogonal properties. Furthermore, we describe the notable properties of parabolas. From then on, we establish important notions in Projective Geometry of inversion, polar correspondence, and, more generally, projective transformation. Afterward, we describe the main projective properties of the circle, extending them to conics. Finally, we propose construction activities based on the concepts and properties of Projective Geometry of Conics, developed in advance, aiming for an interactive and dynamic approach. Thus, we present the possibilities of expanding students' knowledge about geometric transformations beyond Euclidean Geometry, with GeoGebra as the main tool in the teaching and learning process