A generalization of a two triangle inequality
The author proves that for any two simplices \(s^{(n)}\) and \(s^{'(n)}\) in \(E^ n\), \[ D^ 2\geq n^ 4V^{n/2}(s^{(n)})\cdot V^{(2n- 2)/2}(s^{'(n)}) \] where V(W) denotes the volume of the simplex W and \(D=\sum^{n+1}_{i=1}x_ iV(s_ i^{'(n-1)})\), \(x_ i\) being the distance of the ith vertex \(A_ i\) of \(s^{(n)}\) from an interior point M; and \(s_ i^{'(n-1)}\) is the facet \((A'_ 1A'_ 2...A'_{i- 1}A'_{i+1}...A'_{n+1})\) of \(s^{'(n)}.\) This is a generalization of one of the inequalities proved for a triangle by Bottema and Klamkin in 1974.
scientific article; zbMATH DE number 4175875