Generalization of Ceva theorem

2025/08/16 by Wojciech Wdowski, Wdowski, Wojciech
Mathematics · #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2508.11853

Abstract

In this paper, we present a novel generalization of the classical Ceva theorem to arbitrarily dimensional simplexes. Our approach allows cevians to have any dimension (smaller than the dimension of the base simplex). Consequently, our result unifies other generalizations of the Ceva theorem obtained in recent years.

Related

• Ceva's triangle inequalities
• A generalization of Forelli's theorem
• Triangles and groups via cevians
• An Elementary Proof of the 3 Dimensional Simplex Mean Width Conjecture
• An elementary approach to simplexes in thin subsets of Euclidean space