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 -