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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also re-obtainthe 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 $\mathbb{D}$.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, we define a base curve, a rolling curve and a roulette on generalized complex number plane ($\mathfrak{p}$-complex plane) $\mathbb{C}_{J}$.
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Key Findings & Data:We examine the third one of these curves under the condition that two others given.
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Conclusion & Impact:We also re-obtainthe 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 $\mathbb{D}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:base curve · rolling curve · roulette
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-obtainthe 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 $\mathbb{D}$.
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Cite This Article
AKBIYIK, M., GÜRSES, N., YÜCE, S. (2019). A Survey on the Base, Rolling and Roulette Curves on Generalized Complex Number Plane $\mathbb{C}_{J}$. Konuralp Journal of Mathematics, Cilt: 7 Sayı: 1, 228–232. https://ajindex.com/articles/908890