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arXiv · 2507.10067

The Maximum of the Volume of a Cevian Simplex and its Parts

Yagub N. Aliyev
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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 $\frac{1}{4}$ 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 $\frac{1}{4}$ replaced by $\frac{1}{n^n}$, using barycentric coordinates. We also use this method to solve two optimization problems about the parts of this simplex.

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Yagub N. Aliyev. 2025-07-14. The Maximum of the Volume of a Cevian Simplex and its Parts. https://arxiv.org/abs/2507.10067

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