Meaningful Learning of University Students About the Normal Curvature of the Implicitly Given Hyperbolic Paraboloid Based on GeoGebra

Jiménez-Vilcherrez J.; Castillo-Aguilera E.; Vicente-Morocho A.; Velezmoro-León R.; Ipanaqué-Chero R. · CEUR Workshop Proceedings (2023)

Resumen

Achieving significant learning in teaching Geometry in three-dimensional space to undergraduate students is a challenge for the teacher since it always requires a very high level of abstraction in students to visualize mathematical objects, which is often very difficult. difficult. But in recent years, as a result of the pandemic, the use of virtual tools has accelerated, developing skills of both teachers and students in the management of technological resources for teaching mathematics that help strengthen meaningful learning; One of these tools is GeoGebra, which enhances the teaching of geometry in the classroom by providing students with a graphic visualization from three different points of view and allows them to develop their creativity and autonomy in the search for knowledge. This article aims to analyze the normal curvature at all points of the hyperbolic paraboloid given implicitly from the shape operator, answering the questions of undergraduate students, specifically in the students of the Differential Geometry course of the mathematics specialty, given that Generally, in the existing literature of the course, only the normal curvature at the origin is calculated. To achieve this, first two tangent vector fields were inferred to the hyperbolic paraboloid given implicitly, then the shape operator and the normal curvature were calculated at all points of the hyperbolic paraboloid given implicitly and finally the deduced formulas were implemented in GeoGebra using the The use of some specific commands allowed us to obtain a real-time graphical visualization of the analysis of the normal curvature at all points of the saddle, given implicitly, from the shape operator. It may be possible to present examples of the calculation and graphic display of the normal curvature at some points on the surface other than the origin, presenting a contribution to the understanding of the topic.

Instituciones: Universidad Nacional de Piura; Universidad Tecnológica del Perú