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

  • Identification data

    Identifier: imarina:9262320
    Authors:
    Herrera BTran QH
    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 Thébault’s theorem.We establish a link between the radical center of the four spheres, the insphere, and the Monge point of a tetrahedron.
  • Others:

    Author, as appears in the article.: Herrera B; Tran QH
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Herrera Gómez, Blas
    Keywords: Thébault’s theorem Tetrahedron Solid geometry Radical center of spheres Monge point Insphere thebault's theorem tetrahedron radical center of spheres monge point insphere
    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 Thébault’s theorem.We establish a link between the radical center of the four spheres, the insphere, and the Monge point of a tetrahedron.
    Thematic Areas: Mathematics Mathematical physics Geometry and topology Applied mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: blas.herrera@urv.cat
    Author identifier: 0000-0003-2924-9195
    Record's date: 2024-09-07
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://dergipark.org.tr/en/pub/iejg/issue/69397/957190
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: International Electronic Journal Of Geometry. 15 (1): 75-78
    APA: Herrera B; Tran QH (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. DOI: 10.36890/IEJG.957190
    Article's DOI: 10.36890/IEJG.957190
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2022
    Publication Type: Journal Publications
  • Keywords:

    Applied Mathematics,Geometry and Topology,Mathematical Physics,Mathematics
    Thébault’s theorem
    Tetrahedron
    Solid geometry
    Radical center of spheres
    Monge point
    Insphere
    thebault's theorem
    tetrahedron
    radical center of spheres
    monge point
    insphere
    Mathematics
    Mathematical physics
    Geometry and topology
    Applied mathematics
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