The Maximum of the Volume of a Cevian Simplex and its Parts
Abstract
The Cevian triangle corresponding to an interior point M of a triangle is the triangle determined by the feet of the three Cevians concurrent at M. It is known that the area of the Cevian triangle for an interior point M of a triangle is at most 14 of the area of the triangle, with maximum attained when M is the triangle’s centroid. This can be generalized from triangles to n-dimensional simplices, with 14 replaced by 1nn, using barycentric coordinates. We also use this method to solve two optimization problems about the parts of this simplex.
Fields of Study & Subjects
Point processes and geometric inequalities
Mathematics and Applications
Analytic Number Theory Research
Publication details
- Journal / source
- American Mathematical Monthly
- Publisher
- Informa UK Limited
- Pages
- 1–5
- Publication date
- 28 August 2026
- Language
- EN