On the Grace-Danielsson inequality for tetrahedra

Abstract

The difference between the (squared) sides of the Grace-Danielsson inequality for tetrahedra will be represented as a sum of two nonnegative terms. This gives another proof of the inequality. Examining the denominator allows us to characterize the infinite triangular prism as a degenerate tetrahedron. We give conditions for equality (for a zero gap) as well, and some examples are included.

12 pages, 2 figures

References in corpus (1)

• The Euler and Grace-Danielsson inequalities for nested triangles and tetrahedra: a derivation and generalisation using quantum information theory