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Year 2022, , 75 - 78, 30.04.2022

Blas Herrera Quang Hung Tran

https://doi.org/10.36890/iejg.957190
Cited By: 1

Abstract

References

  • [1] Akopyan, A. V.: Some Remarks on the Circumcenter of Mass. Discrete Comput. Geom. 51, 837–841 (2014).
  • [2] Altshiller-Court, N.: Modern Pure Solid Geometry. Chelsea Publications. New York (1964).
  • [3] Herrera, B.: Two conjectures of Victor Thebault linking tetrahedra with quadrics. Forum Geom. 15, 115–122 (2015).
  • [4] Leopold, U., Martini, H.: Monge Points, Euler Lines, and Feuerbach Spheres in Minkowski Spaces. In: Conder M., Deza A.,Weiss A. (eds) Discrete Geometry and Symmetry. GSC 2015. Springer Proceedings in Mathematics & Statistics, 234. Springer, Cham.
  • [5] Thebault, V.: Problem 4368, Amer. Math. Monthly. 56, 637 (1949).
  • [6] Thebault, V.: Problem 4530. Amer. Math. Monthly. 60, 193 (1953).
  • [7] Weisstein, E. W.: Monge Point. MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/MongePoint.html.
  • [8] Weisstein, E. W.: Monge’s Tetrahedron Theorem. MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/ MongesTetrahedronTheorem.html.
  • [9] Weisstein, E. W.: Sphere. MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/Sphere.html.

An Analogue of Thébault's Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron

Year 2022, , 75 - 78, 30.04.2022

Blas Herrera Quang Hung Tran

https://doi.org/10.36890/iejg.957190
Cited By: 1

Abstract

In 1953, Victor Thébault conjectured a link between the altitudes of a tetrahedron and the radical center of the four spheres with the centers at the vertices of this tetrahedron and the corresponding tetrahedron altitudes as radii. This conjecture was proved in 2015. In this paper, we propose an analogue of Th\'{e}bault's theorem. We establish a link between the radical center of the four spheres, the insphere, and the Monge point of a tetrahedron.

Keywords

Solid geometry Thébault's theorem tetrahedron radical center of spheres Monge point insphere

References

  • [1] Akopyan, A. V.: Some Remarks on the Circumcenter of Mass. Discrete Comput. Geom. 51, 837–841 (2014).
  • [2] Altshiller-Court, N.: Modern Pure Solid Geometry. Chelsea Publications. New York (1964).
  • [3] Herrera, B.: Two conjectures of Victor Thebault linking tetrahedra with quadrics. Forum Geom. 15, 115–122 (2015).
  • [4] Leopold, U., Martini, H.: Monge Points, Euler Lines, and Feuerbach Spheres in Minkowski Spaces. In: Conder M., Deza A.,Weiss A. (eds) Discrete Geometry and Symmetry. GSC 2015. Springer Proceedings in Mathematics & Statistics, 234. Springer, Cham.
  • [5] Thebault, V.: Problem 4368, Amer. Math. Monthly. 56, 637 (1949).
  • [6] Thebault, V.: Problem 4530. Amer. Math. Monthly. 60, 193 (1953).
  • [7] Weisstein, E. W.: Monge Point. MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/MongePoint.html.
  • [8] Weisstein, E. W.: Monge’s Tetrahedron Theorem. MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/ MongesTetrahedronTheorem.html.
  • [9] Weisstein, E. W.: Sphere. MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/Sphere.html.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Blas Herrera This is me 0000-0003-2924-9195

Quang Hung Tran 0000-0003-2468-4972

Publication Date April 30, 2022
Acceptance Date March 25, 2022
Published in Issue Year 2022

Cite

APA Herrera, B., & Tran, Q. H. (2022). An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron. International Electronic Journal of Geometry, 15(1), 75-78. https://doi.org/10.36890/iejg.957190
AMA Herrera B, Tran QH. An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron. Int. Electron. J. Geom. April 2022;15(1):75-78. doi:10.36890/iejg.957190
Chicago Herrera, Blas, and Quang Hung Tran. “An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres With the Insphere and the Monge Point of a Tetrahedron”. International Electronic Journal of Geometry 15, no. 1 (April 2022): 75-78. https://doi.org/10.36890/iejg.957190.
EndNote Herrera B, Tran QH (April 1, 2022) An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron. International Electronic Journal of Geometry 15 1 75–78.
IEEE B. Herrera and Q. H. Tran, “An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron”, Int. Electron. J. Geom., vol. 15, no. 1, pp. 75–78, 2022, doi: 10.36890/iejg.957190.
ISNAD Herrera, Blas - Tran, Quang Hung. “An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres With the Insphere and the Monge Point of a Tetrahedron”. International Electronic Journal of Geometry 15/1 (April 2022), 75-78. https://doi.org/10.36890/iejg.957190.
JAMA Herrera B, Tran QH. An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron. Int. Electron. J. Geom. 2022;15:75–78.
MLA Herrera, Blas and Quang Hung Tran. “An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres With the Insphere and the Monge Point of a Tetrahedron”. International Electronic Journal of Geometry, vol. 15, no. 1, 2022, pp. 75-78, doi:10.36890/iejg.957190.
Vancouver Herrera B, Tran QH. An Analogue of Thébault’s Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron. Int. Electron. J. Geom. 2022;15(1):75-8.

Cited By

$$n$$-Dimensional Generalizations of a Thébault Conjecture
Mathematical Notes
https://doi.org/10.1134/S0001434624030337