A Survey on the Base, Rolling and Roulette Curves on Generalized Complex Number Plane $\mathbb{C}_{J}$

Abstract

In this study, we define a base curve, a rolling curve and a roulette on generalized complex number plane ($\mathfrak{p}$-complex plane) $\mathbb{C}_{J}$. We examine the third one of these curves under the condition that two others given. We also re-obtain

the Euler Savary's formula in $\mathbb{C}_{J}$ as a generalization of the Euler Savary's formula for complex plane $\mathbb{C}$, hyperbolic plane $\mathbb{H}$ and dual plane $\mathbb{D}$.

Keywords

• base curve,rolling curve,roulette,associated curve,Generalized complex number plane

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