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

Authors : Mücahit AKBIYIK, Nurten GÜRSES, Salim YÜCE

Pages : 228-232

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Publication Date : 2019-04-15

Article Type : Research Paper

Abstract :In this study, we define a base curve, a rolling curve and a roulette on  generalized complex number plane insert ignore into journalissuearticles values($\mathfrak{p}$-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