Uma abordagem da Cicloide: "a Helena da geometria"

Abstract

This work presents a brief historical research on the cycloid, in addition to an intuitive construction on the curve, working on the definition and parameterization. This research discusses pedagogical practices that link the contents to the playful context of presenting the cycloid and not just algebraic as in calculation books. Taking into account the context of Mathematics, this proposal presents as a problem the lack of interest in the study of the curve, considering that its use was left aside by mathematicians. In the context of these problems, the proposal intends to awaken the relevance of the cycloid, answering the following questions: how to motivate the understanding of the cycloid? How to show practicality through your application? The main objective of the proposal is to present in a more practical way the understanding of the cycloid. This work is based on studies by Boyer (2012), Bustillo and Sassine (2011) and Stewart (2013). With the results, it was possible to observe that although we have other ways to calculate the cycloid, the best way would be with the parametric equations, as they bring us a simpler way of calculating the curve. The results also point to the practicality of building in Geogebra.