2025/07/14 by Yagub N. Aliyev, Aliyev, Yagub N.
Mathematics · #51M04 #51M05 #51M16 #51M25 #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2507.10067
openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (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 (1)/(4) replaced by (1)/(nn), using barycentric coordinates. We also use this method to solve two optimization problems about the parts of this simplex.