The Maximum of the Volume of a Part of a Cevian Simplex

Abstract

The cevians passing through a point in a simplex create a cevian simplex, which is divided by these cevians into smaller simplices. We consider the problem about the maximum of the ratio of the sum of the volumes of some of these smaller simplices by the volume of the reference simplex. The special case of tetrahedron is given as an example.