Journal for Geometry and Graphics 24 (2020), No. 2, 193--196
Copyright Heldermann Verlag 2020
Geometric Inequalities on Parallelepipeds and Tetrahedra
Alana Bailey
San Jose State University, San Jose, CA 95192, U.S.A.
alana.bailey@sjsu.edu
Hidefumu Katsuura
San Jose State University, San Jose, CA 95192, U.S.A.
hidefumi.katsuura@sjsu.edu
We prove an inequality comparing the sum of areas of faces of a parallelepiped to its volume. Then we prove an inequality on a tetrahedron analogous to Weitzenb\"ock's Inequality on a triangle using the inequality on a parallelepiped and Yetter's Theorem. We also give a short proof of Yetter's Theorem.
Keywords: Weitzenboeck's inequality, parallelepiped, tetrahedron, Yetter's Theorem.
MSC: 51M16; 51M25
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