Curvas planas, curvas no espaço e aplicação

Abstract

This work aims to study curves in the plane and in space and their applications. For this, a study of the necessary preliminary concepts of Differential Geometry will be carried out. Then, the results of a curve parameterized by the arc length, Frenet reference for a curve parameterized by the arc length, Frenet reference for a curve not parameterized by the arc length, curvature, torsion and the Fundamental Theorem of Flat Curves will be enunciated and demonstrated. With this study, it became possible to develop applications with commands and animations in the Geogebra Software on Tangent Vector, reparametrization of the curve, curve reparametrized by the arc length, curve is a helix, curvature, maximum curvature and the Fundamental Theorem of Flat Curves. Therefore, the study of curves in the plane and in space is important in Differential Geometry and also in other areas such as Differential and Integral Calculus and made it possible with the Geogebra Software to understand the algebraic and geometric part.