Inequalities for volumes and medians of two simplexes (Q710990)

The Neuberg-Pedoe inequality first appeared in an article by \textit{D. Pedoe} in [Proc. Camb. Phil. Soc. 38, 397--398 (1942; Zbl 0060.34715)], and is distinguished in that it is an inequality among the areas and side lengths of \textit{two} triangles. Generalizations to simplices in higher dimensions are made by \textit{L. Yang} and \textit{J. Z. Zhang} in [Bull. Aust. Math. Soc. 27, 203--214 (1983; Zbl 0519.51013)] and by \textit{G. S. Leng} in [Geom. Dedicata 68, No. 1, 43--48 (1997; Zbl 0890.51016)], and by others. The paper under review establishes more generalizations that involve the volumes and lengths of medians of two simplices in any dimension.