O ensino das cônicas através de estudos contextualizados até sua concepção na geometria analítica: parábola

Abstract

Conics are currently used in astronomy, engineering, architecture, physics and many other areas. However, the study of conics is restricted to high school and, in most cases, not even then. Conics are taught, in many textbooks, only by memorizing formulas, without understanding the properties and concepts behind them. Apollonius was the first to deepen in the study of conics. Kepler established that the planets’ orbits were elliptical and, since then, ellipses have gained importance in astronomy. It is also used in the construction of reflectors and whispering chambers, which use its properties of reflection in the focus. The hyperbole method is used in the LORAN navigation method (long-range navigation) and in the description of an alpha-particle subject to an electrical field generated by an atomic nucleus. The parabola is used in the fabrication of satellite dishes, head lights, reflectors, among others. The parabolas are models of various types of movements and are vastly used in physics. We suggest that conics must be taught in a manner of easer visualization using concrete material and, after this, teach the definitions. In order to do this, we bring some interesting activities to work with in the classroom. We also bring, in chapter 5, a portion on coordinate transformations focusing on graduate courses. With this we aim at leading the high school student to be interested in and understand conics.