
Journal for Geometry and Graphics 23 (2019), No. 2, 179182 Copyright Heldermann Verlag 2019 ThreeDimensional 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: Threedimensional Viviani Theorem, equifacial tetrahedron, isosceles tetrahedron. MSC: 51N20; 52B10 [ Fulltextpdf (87 KB)] 