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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2023 / Volume: 72 Issue: 4

Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$

Süleyman Şenyurt(ORDU ÜNİVERSİTESİ)0000-0003-1097-5541
Davut Canlı(ORDU UNIVERSITY)0000-0003-0405-9969
Elif Çan(ORDU UNIVERSITY)0000-0001-5870-114X
Sümeyye Gür Mazlum(GUMUSHANE UNIVERSITY)0000-0003-2471-1627
Pages
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Publication Date
2023-12-29
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AI Summary & Key Takeaways

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

Finally, as an example, we obtain ruled surfaces whose base curves are Viviani’s curves and plot the graphics of these surfaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve.
📊
Key Findings & Data:In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces.
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Conclusion & Impact:Finally, as an example, we obtain ruled surfaces whose base curves are Viviani’s curves and plot the graphics of these surfaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Smarandache curve · ruled surfaces · mean curvature

Abstract

In this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve. Then, we construct new ruled surfaces along these Smarandache curves with the direction vectors obtained from the Frenet vectors and the Darboux vector, and give the equations of these surfaces. In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces. Finally, as an example, we obtain ruled surfaces whose base curves are Viviani’s curves and plot the graphics of these surfaces.

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Cite This Article

Şenyurt, S., Canlı, D., Çan, E., Mazlum, S. G. (2023). Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 4. https://doi.org/10.31801/cfsuasmas.1151064

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