Parametrização de curvas planas, cicloide e os problemas da braquistócrona e da tautócrona : aplicações no ensino médio com a utilização do GeoGebra

Abstract

In this work we will take an approach on flat curves. We begin the development of the studies with the curves that are studied in High School, but, basically using Cartesian equations and their graphical representations. We will approach the subject of these curves using the concept of parametric equations, transforming the study of static elements in the plane into dynamic elements, this approach also makes possible the contact of the secondary students with the calculus and the differential geometry of the undergraduate courses. We will present a study on the Cycloid and two classical problems (Brachistochrona and Tautochrona ) associated with it. Finally, we will present some proposals for activities to be developed in the classroom, which involve constructions of physical structures, calculations and the use of GeoGebra software.