Generalization of Ceva theorem

TL;DR

This paper introduces a new generalization of the classical Ceva theorem to higher-dimensional simplexes, allowing cevians of any dimension and unifying previous generalizations in a comprehensive framework.

Contribution

It presents a novel, unified generalization of Ceva's theorem applicable to arbitrary dimensions and cevians of varying dimensions, extending classical results.

Findings

Unified framework for Ceva theorem in higher dimensions

Applicable to cevians of any dimension less than the simplex

Connects and generalizes recent Ceva theorem extensions

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.