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The Maximum of the Volume of a Cevian Simplex and its Parts
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The Maximum of the Volume of a Cevian Simplex and its Parts
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Paper
The Maximum of the Volume of a Cevian Simplex and its Parts
2026
Overview
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 \\(1n^n\\), using barycentric coordinates. We also use this method to solve two optimization problems about the parts of this simplex.
Publisher
Cornell University Library, arXiv.org
Subject
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