TY - GEN

T1 - Torus of Revolution Generated by Curves of Eight

AU - Velásquez-Fernández, Felícita M.

AU - Vega-Ordinola, Sindy Pole

AU - Silupu-Suarez, Carlos Enrique

AU - Ipanaqué-Chero, Robert

AU - Velezmoro-León, Ricardo

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - Among the geometric bodies of revolution we find the torus of revolution generated from a circumference that rotates around an axis. Given the classic definition used in Mathematics, interest arises in finding other curves that generate the torus of revolution when rotating around an axis. There is already work done, about the construction of toruses of revolution, using a lemniscatic curve. In this article, making the respective analysis and the necessary programming using the Mathematica 11.1 software, allowed us to carry out the necessary calculations and geometric visualizations of the mathematical object: So a torus of revolution was built from the curve of eight in its parametric form and even the equation of the torus in its Cartesian form. The study was extended and the torus of revolution was generated from rational and irrational curves that rotate around an axis. Curves were determined that were on the torus generated by a curve of eight, which when properly projected to planes, curves that have symmetries were obtained. When points on these curves are properly taken, special irregular polygons are obtained. By obtaining these results, a satisfactory answer to the research question was obtained, as well as a way to define it. In addition, it has shown us a wide path of research on the different curves that can generate a torus of revolution.

AB - Among the geometric bodies of revolution we find the torus of revolution generated from a circumference that rotates around an axis. Given the classic definition used in Mathematics, interest arises in finding other curves that generate the torus of revolution when rotating around an axis. There is already work done, about the construction of toruses of revolution, using a lemniscatic curve. In this article, making the respective analysis and the necessary programming using the Mathematica 11.1 software, allowed us to carry out the necessary calculations and geometric visualizations of the mathematical object: So a torus of revolution was built from the curve of eight in its parametric form and even the equation of the torus in its Cartesian form. The study was extended and the torus of revolution was generated from rational and irrational curves that rotate around an axis. Curves were determined that were on the torus generated by a curve of eight, which when properly projected to planes, curves that have symmetries were obtained. When points on these curves are properly taken, special irregular polygons are obtained. By obtaining these results, a satisfactory answer to the research question was obtained, as well as a way to define it. In addition, it has shown us a wide path of research on the different curves that can generate a torus of revolution.

KW - Mathematica

KW - Torus

KW - Turn of eight

UR - http://www.scopus.com/inward/record.url?scp=85135007232&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-10522-7_27

DO - 10.1007/978-3-031-10522-7_27

M3 - Conference contribution

AN - SCOPUS:85135007232

SN - 9783031105210

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

SP - 385

EP - 398

BT - Computational Science and Its Applications - ICCSA 2022 - 22nd International Conference, Proceedings

A2 - Gervasi, Osvaldo

A2 - Murgante, Beniamino

A2 - Hendrix, Eligius M.

A2 - Taniar, David

A2 - Apduhan, Bernady O.

PB - Springer Science and Business Media Deutschland GmbH

T2 - 22nd International Conference on Computational Science and Its Applications, ICCSA 2022

Y2 - 4 July 2022 through 7 July 2022

ER -