Construction of Torus of Revolution Generated from Epicycloids

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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.

Idioma originalInglés
Título de la publicación alojadaComputational Science and Its Applications – ICCSA 2023 - 23rd International Conference, Proceedings
EditoresOsvaldo Gervasi, Beniamino Murgante, David Taniar, Bernady O. Apduhan, Ana Cristina Braga, Chiara Garau, Anastasia Stratigea
EditorialSpringer Science and Business Media Deutschland GmbH
Número de páginas18
ISBN (versión impresa)9783031368073
EstadoPublicada - 2023
Evento23rd International Conference on Computational Science and Its Applications , ICCSA 2023 - Athens, Grecia
Duración: 3 jul. 20236 jul. 2023

Serie de la publicación

NombreLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volumen13957 LNCS
ISSN (versión impresa)0302-9743
ISSN (versión digital)1611-3349


Conferencia23rd International Conference on Computational Science and Its Applications , ICCSA 2023


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