CURVAS PARAMETRIZADAS DIFERENCIÁVEIS: PARAMETRIZAÇÃO DE CURVAS PLANAS E UM TEOREMA GERAL DE CLASSIFICAÇÃO

Abstract

Differential Geometry is a of the main tools for study of differentiable parametrized curves. The present work aims to study the properties of these curves, in plane or in space, using the tools and classical methods of differential and integral calculus. In this sense, the main plane curves discussed here are: Cycloid, Tractrix, Cissoid of Diocles, Catenary, Lemniscate of Bernoulli, Cardioid, Astrouid, Curve of Agnesi, while the main curve in space discussed here is Helix. For this, will be carried out a preliminary detailed theorical study on the differential geometry of the plane and space curves, through results and properties that underlie this theory. Classical concepts such as parameterization of curves, arc length, curvature, torsion and the local Frenet theory will also be discussed here. In conclusion, as the main objective of this work, it is shown by means of a general theorem that some curves in plane and space can be classified by information given on its curvature and its torsion.