Geometria Diferencial com Python: Modelagem de evolutas e involutas de curvas

Abstract

The present work addresses the theme Differential Geometry with Python: modeling of evolutes and involutes of curves, inserted in the context of Differential Geometry, seeking to understand the following research problem: “In what way can the implementation of programming codes in Python contribute to the visualization and understanding of concepts of Differential Geometry, especially regarding the evolutes and involutes of regular curves in Euclidean spaces?”. Thus, the general objective of the study was to implement mathematical models of plane and spatial curves, as well as their evolutes and involutes, using programming codes in Python as a support strategy for the theoretical study of Differential Geometry. To achieve this objective, a qualitative and exploratory research was carried out, with a theoretical-computational approach, using as methodological procedures the bibliographic survey, conceptual study of Differential Geometry, and the implementation of programming codes in Python for simulation and graphical visualization of regular curves. It is therefore concluded that the implementation of Python codes for the evolutes and involutes of curves constitutes an effective resource for the study and deepening of concepts, contributing to a more intuitive learning process, in addition to the possibility of use in other research that investigates different types of curves and Properties.