Curvas planas parametrizadas: uma reflexão metodológica de suas aplicações

Abstract

The parameterization of plane curves has become a method of great importance for the development of mathematics, due to the impossibility of expressing some curves in the form of a single-variable function. Starting from this theme, this work aims to present a methodological and reflective explanation about parameterized curves and their relevance in everyday life through applications. To achieve our objectives, the methodology used in the elaboration of this work was the explanatory one, where we deepen the study of the parameterized plane curves through vast bibliographic research of specific and complementary material. Thus, we will approach the historical context that led to its improvement, through some notable mathematicians such as Descartes and Fermat. Usually, in the study of Cartesian curves, we adopt only one dependent variable and one independent variable (Y = f(x)), but we come across situations in which there are curves that are often difficult or even impossible to express explicitly by a function of a single variable. In this case, we need another variable, called a “parameter”, which helps us to better explain the curves, that is, the parameterized curves. Therefore, in this work, we present the characterization of parametric curves and some techniques for sketching such curves. We also deal with some notable curves, such as the Cycloid and Epicycloids and some applications of the curves in everyday life. Furthermore, this research has as target public students in the final years of high school and beginning students of undergraduate courses in mathematics the licentiate, who seek a better understanding of the applicability of mathematics in a concrete way in everyday life, and thus an expanded view of the discipline.