Construction of Torus of Revolution Generated from Epicycloids

Flores-Cordova D.A.; Arellano- Ramírez C.E.; Ipanaqué-Chero R.; Velásquez-Fernández F.M.; Velezmoro-León R. · Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2023) · DOI: 10.1007/978-3-031-36808-0_5

Resumen

Among the geometric bodies of revolution, the torus of revolution stands out, which can be generated from a circumference, lemniscate curves and the figure-of-eight curve. Given the classical definition used in Mathematics, interest arises in finding other curves that generate the torus of revolution when rotating around an axis. In this article, carrying out the respective analyzes and the necessary programming using the Mathematica software, allowed us to carry out the necessary calculations and geometric visualizations of the mathematical object: This is how a torus of revolution was built from epicycloid curves in their parametric form. The study was extended by determining curves that were on the torus generated by epicycloid curves, which when properly projected to planes, curves that present beautiful symmetries were obtained. When the points of these curves are taken correctly, special irregular polygons are obtained. With the obtaining of these results, a satisfactory answer to the research question was obtained, as well as a way of defining it. In addition, it has shown us a wide path of research on the different curves that a torus of revolution can generate.

Instituciones: Universidad Nacional de Piura