Holditch-Type Theorem for Non-Linear Points in Generalized Complex Plane $\mathbb{C}_{p}$

Abstract

The generalized complex number system and generalized complex plane were studied by Yaglom [22], [23] and Harkin [7]. Moreover, Holditch-type theorem for linear points in $\mathbb{C}_{p}$ were given by Eri\c{s}ir et al. [6]. The aim of this paper is to find the answers of the questions ''How is the polar moments of inertia calculated for trajectories drawn by non-linear points in $\mathbb{C}_{p}$?'', ''How is Holditch-type theorem expressed for these points in $\mathbb{C}_{p}$?'' and finally ''Is this paper a new generalization of [6]?''.