Journal for Geometry and Graphics 30 (2026), No. 1, 089--096
Copyright by the authors licensed under CC BY SA 4.0
The Maximum of the Volume of a Part of a Cevian Simplex
Zamina E. Guliyeva
ADA University, Baku, Azerbaijan
zeguliyeva@ada.edu.az
Yagub N. Aliyev
ADA University, Baku, Azerbaijan
yaliyev@ada.edu.az
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 of maximizing the ratio of the sum of the volumes of some of these smaller simplices to the volume of the reference simplex. An analogous question concerning the product of the volumes is also considered. The special case of the tetrahedron is presented as an example.
Keywords: Simplex, volume, cevian, barycentric coordinates, optimization.
MSC: 51M16; 26D07, 51M25.
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