Geodesic
Three-Dimensional Viviani Theorem on a Tetrahedron
Journal for geometry and graphics, Tome 23 (2019) no. 2, pp. 179-182.

Voir la notice de l'article provenant de la source Heldermann Verlag

A theorem of Viviani states that the sum of the distances from an inside point to the sides of a triangle is constant if, and only if the triangle is equilateral. It has a more general version that deals with a point anywhere in the plane. We will give a theorem similar to this general Viviani Theorem on a tetrahedron.
Classification : 51N20, 52B10
Mots-clés : Three-dimensional Viviani Theorem, equifacial tetrahedron, isosceles tetrahedron 
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     author = {H. Katsuura },
     title = {Three-Dimensional {Viviani} {Theorem} on a {Tetrahedron}},
     journal = {Journal for geometry and graphics},
     pages = {179--182},
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     volume = {23},
     number = {2},
     year = {2019},
     url = {http://geodesic.mathdoc.fr/item/JGG_2019_23_2_JGG_2019_23_2_a3/}
}
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H. Katsuura . Three-Dimensional Viviani Theorem on a Tetrahedron. Journal for geometry and graphics, Tome 23 (2019) no. 2, pp. 179-182. http://geodesic.mathdoc.fr/item/JGG_2019_23_2_JGG_2019_23_2_a3/