Curvas descritas mecanicamente e GeoGebra: uma proposta destinada ao ensino médio

Abstract

This piece of work has as its main objective to approach the mechanically described curves as a proposal to high school. This focus is justified by the fact of the geometric constructions which generate each curve are an opportunity to explore elements, properties and relations of euclidean geometry, topics where difficulties in the teaching-learning process are found in basic school. On the other hand, the curves obtained by parametric equations are examples of relevant situations to make a parallel reasoning between the analytical geometry and the euclidean geometry. Some activities facing high school students are proposed here, which explore rolling curves (hypocycloid , epicycloid , cycloid and involute of the circle) and the the mechanisms that generate linear motion from circular motion (Peaucellier and Hart). The use of a dynamic geometry software, in this case the Geogebra, is essencial to the development to the activities because it allows the construction which generates each curve, promoting the stability of relations between the elements for the move action. A research about the teaching subjects related to mechanically described curves and the conceptual aspects about the rolling curves and the mechanisms that generate linear motion from circular motion are made here to support the aplication to the suggested activities. A discussion about the possible objectives which can be achieved with each kind of activity is also made here.