Propuesta de abordaje transversal del concepto diferencial de curvatura en situaciones f\'isicas

TL;DR

This paper presents an inclusive, applied approach to the differential curvature concept using Newton's mechanics problems to enhance the modeling versatility of derivatives and to teach classic physics topics through curvature.

Contribution

It introduces a novel didactic proposal integrating differential curvature into physics education, emphasizing its versatility in modeling and understanding physical systems.

Findings

Enhanced understanding of curvature in physical contexts

Improved teaching methodology for derivatives in physics

Application of curvature concepts to classic physics topics

Abstract

During the process of teaching the concept of derivative, it is common and natural to refer to geometric interpretations, such as the use of the tangent line and the maximum and minimum points of a function, to illustrate the scope of the derivative. In this work, an inclusive and applied way of the concept of curvature differential is presented, specifically with the intervention of problems of Newton's mechanics, whose purpose is double, on the one hand, to provide the derivative with a highly versatile sense to model systems, and on the other hand; to approach diverse classic topics of the initial physics courses from a didactic proposal centered on the concept of curvature.