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Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2020 / Cilt: 16 - Sayı: 1

Ruled Surfaces Constructed by Planar Curves in Euclidean 3-Space with Density

Ahmet Kazan
H. Bayram Karadağ
Mustafa Altın
Pages
81–88
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We useMathematica when we are plotting the graphs of examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present study, firstly we recall the parametric expressions of planar curves with zero 𝜑-curvaturein Euclidean 3-space with density 𝑒𝑎𝑥1 and with the aid of the Frenet frame of these planar curves, weobtain the Smarandache curves of them.
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Key Findings & Data:After that, we study on ruled surfaces which are constructed bythe curves with zero 𝜑-curvature in Euclidean 3-space with density 𝑒𝑎𝑥1 and their Smarandache curvesby giving the striction curves, distribution parameters, mean curvature and Gaussian curvature of theseruled surfaces.
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Conclusion & Impact:We useMathematica when we are plotting the graphs of examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In the present study, firstly we recall the parametric expressions of planar curves with zero 𝜑-curvaturein Euclidean 3-space with density 𝑒𝑎𝑥1 and with the aid of the Frenet frame of these planar curves, weobtain the Smarandache curves of them. After that, we study on ruled surfaces which are constructed bythe curves with zero 𝜑-curvature in Euclidean 3-space with density 𝑒𝑎𝑥1 and their Smarandache curvesby giving the striction curves, distribution parameters, mean curvature and Gaussian curvature of theseruled surfaces. Also, we give some examples for these surfaces by plotting their graphs. We useMathematica when we are plotting the graphs of examples.

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Cite This Article

Kazan, A., Karadağ, H. B., Altın, M. (2022). Ruled Surfaces Constructed by Planar Curves in Euclidean 3-Space with Density. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 16 - Sayı: 1, 81–88. https://ajindex.com/articles/472179

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