Geometria diferencial das curvas planas

Abstract

This work present in an objective way what would be differential geometry base: the plane curves. At first, the basic definitions, considered very important for the study of plane curves,were presented, as how to define what is a parametrized curve, how to find tangent vectors of a curve, the definition of regular curve and arc length. From this, it is possible to proceed to the definition of Frenet formulas in the plane. Therefore, the necessary tools to enunciate and prove a very important theorem in differential geometry, the Fundamental Theorem of the Plane Curves,are obtained. Finally, other two theorems will be presents, that also stand out in differential geometry, the Jordan’s Curve Theorem and the Isoperimetric Inequality.