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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

Mustafa ALTIN
Ahmet KAZAN
H.bayram KARADAĞ
Pages
81–88
Publication Date
2020-03-27
DOI
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AI Summary & Key Takeaways

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

We use Mathematica when we are plotting the graphs of examples.

📌 3 Key Takeaways

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Objective & Hypothesis:In the present study, firstly we recall the parametric expressions of planar curves with zero phi-curvature in Euclidean 3-space with density e^ax_1 and with the aid of the Frenet frame of these planar curves, we obtain the Smarandache curves of them.
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Key Findings & Data:After that, we study on ruled surfaces which is constructed by curves with zero -curvature in Euclidean 3-space with density e^ax_1 and their Smarandache curves by giving the striction curves, distribution parameters, mean curvature and Gaussian curvature of these ruled surfaces.
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Conclusion & Impact:We use Mathematica when we are plotting the graphs of examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ruled surfaces · Smarandache curves · Weighted curvature

Abstract

In the present study, firstly we recall the parametric expressions of planar curves with zero phi-curvature in Euclidean 3-space with density e^ax_1 and with the aid of the Frenet frame of these planar curves, we obtain the Smarandache curves of them. After that, we study on ruled surfaces which is constructed by curves with zero -curvature in Euclidean 3-space with density e^ax_1 and their Smarandache curves by giving the striction curves, distribution parameters, mean curvature and Gaussian curvature of these ruled surfaces. Also, we give some examples for these surfaces by plotting their graphs. We use Mathematica when we are plotting the graphs of examples.

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Cite This Article

ALTIN, M., KAZAN, A., KARADAĞ, H. (2020). 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/88597

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