TY - GEN

T1 - Construction of Torus of Revolution Generated from Epicycloids

AU - Flores-Cordova, Daniel A.

AU - Arellano- Ramírez, Carlos E.

AU - Ipanaqué-Chero, Robert

AU - Velásquez-Fernández, Felícita M.

AU - Velezmoro-León, Ricardo

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Torus

KW - epicycloides

KW - revolution

UR - http://www.scopus.com/inward/record.url?scp=85165111544&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-36808-0_5

DO - 10.1007/978-3-031-36808-0_5

M3 - Conference contribution

AN - SCOPUS:85165111544

SN - 9783031368073

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 66

EP - 83

BT - Computational Science and Its Applications – ICCSA 2023 - 23rd International Conference, Proceedings

A2 - Gervasi, Osvaldo

A2 - Murgante, Beniamino

A2 - Taniar, David

A2 - Apduhan, Bernady O.

A2 - Braga, Ana Cristina

A2 - Garau, Chiara

A2 - Stratigea, Anastasia

PB - Springer Science and Business Media Deutschland GmbH

T2 - 23rd International Conference on Computational Science and Its Applications , ICCSA 2023

Y2 - 3 July 2023 through 6 July 2023

ER -