Cônicas e quádricas : uma abordagem didática para a ampliação do ensino médio e aprimoramento de cursos técnicos

Abstract

This work was elaborated in order to help teachers and high school students and technical courses such as Industrial automation, shipbuilding, buildings, electrical and electronics to appropriate the spatial vision, as well as algebraic concepts that involve the conical curves and the quadrics surfaces because, given the great difficulty found in relating contents of planar, spatial and analytical geometry with the objects and tools that are applied in their respective courses, nothing better than a approximation of these axes so that one can sharpen the curiosity in a work that allows to improve their student and professional skills. To this end, we will make a brief history and theoretical foundation on the topic reporting the main scholars and their respective contributions. We will deduce the canonical equations with the aid of concepts studied in linear algebra and classify all the conical curves and quadrics surfaces as well as their degenerated from the signs and values of the coefficients and the independent term and still we will construct, with the help of Geogebra, examples of their respective graphs. Finally, we will show the details of an intervention made with the students "volunteers" of the courses already cited, with the use of concrete material, stressing that they were willing to study a little more of the subject in an extra class environment. Animations of the tapered curves, the quadrics surfaces and the justified justifications in addition to the constructions with recyclable material, were elements of this successful intervention.