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Journal for Geometry and Graphics 23 (2019), No. 2, 179--182
Copyright Heldermann Verlag 2019

Three-Dimensional Viviani Theorem on a Tetrahedron

Hidefumi Katsuura
Dept. of Mathematics and Statistics, San Jose State University, 1 Washington Square, San Jose, CA 95192, U.S.A.

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.

Keywords: Three-dimensional Viviani Theorem, equifacial tetrahedron, isosceles tetrahedron.

MSC: 51N20; 52B10

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