Conceptual contributions to the determination of the curvature in Engineering courses

Abstract

Differential geometry began with the study of the characteristics of planar curves, then the behavior of the curves in space was analyzed, which led to the postulates of Frenet, and hence differential geometry evolved due to the contributions of Gauss. At the highly specialized undergraduate courses, most of the literature presents this topic based on definitions, which can be understood with some difficulty by both students and even some teachers. This work presents a detailed description of the terms defined in the concept of curvature. It is of great importance that students from engineering courses understand this concept with certainty and confidence, because it will allow perceiving abstract terms, such as radius of curvature, osculating circle, normal vector; thus, they will have complete handling in the basic description of the movement of bodies. Some examples are presented.