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.
hidefumi.katsuura@sjsu.edu
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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