In this study, we will introduce arithmetical operations on dual hyperbolic numbers wx y ju jv
ε ε=+++ and hyperbolic complex numbers wx iy ju ijv=+++ which forms a commutative ring …

Abstract Let E^ 2 _ 1 E 1 2 be the real 2-dimensional pseudo-Euclidean space of index 1, O
(1; 1) be the group of all pseudo-orthogonal transformations of E^ 2 _ 1 E 1 2 and SO (1; 1) …

In this paper, we introduce one-parameter homothetic motions in the generalized complex
number plane (p p-complex plane) C _ J=\left {x+ Jy:\,\,\, x, y ∈ R,\quad J^ 2= p,\quad p ∈ …

In this study, we firstly give the basic notations of the generalized complex number plane (p
p-complex plane) C _ p C p. Then, we introduce the one-parameter planar motions in p p …

In 10 one-parameter planar motion was first introduced and the relations between absolute,
relative, sliding velocities (and accelerations) in the Euclidean plane\mathbb E^ 2 were …

In this study, the planar kinematics has been studied in a generalized complex plane which
is a geometric representation of the generalized complex number system. Firstly, the planar …

Cp. Then, Holditch-type theorem that express the relationship among the polar moments of
inertia of points has been given for homothetic motion in Cp. Moreover, the some geometric …

Muller, HR [2], on the Euclidean plane E-2, introduced the one-parameter planar motion and
obtained the relation between absolute, relative, sliding velocities (and accelerations). Also …

We expressed the higher‐order velocities, accelerations, and poles under the one‐
parameter planar hyperbolic motions and their inverse motions. The higher‐order …

In this study, the planar kinematics is studied in generalized complex plane which is a
geometric representation of the generalized complex number system. Firstly, the one …