Geogebra como recurso facilitador do processo de ensino-aprendizagem de curvas planas

Abstract

The objective of this work is to contribute to the teaching-learning process of planas curves, in high school as wellas in higher education. To achieve this goal, we present the concepts, de_nitions and studies of planas curves, addressing algebra and geometry through Geogebra Software. Using this tool, we will approach mechanically generated curves (roulettes) and discuss some concepts. The theme provides us with a re_ection on the use of Geogebra software as a facilitating tool in the teaching-learning process. The possibility of being able, on a single screen, to analyze the algebraic and geometric behavior of planas curves contributes to the construction of mathematical knowledge. To this end, we will conduct a brief discussion on the use of Geogebra Software in teaching. Then we will present the main concepts of _at curves such as parameterization, tangent vector, normal vector, Frenet system, arc length, reparametrization, curvature, evolute and involute. In the discussion of all these concepts, Geogebra is present, in order to assist in the discussion and to show the possibilities of its use. Finally, we discuss a proposed activity in the classroom.