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Volume 13
Issue 9
10.3390/math13091526
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Article

On the Special Viviani’s Curve and Its Corresponding Smarandache Curves

by
Yangke Deng
1,
Yanlin Li
1,*,
Süleyman Şenyurt
2,
Davut Canlı
2 and
İremnur Gürler
2
1
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2
Department of Mathematics, Ordu University, Ordu 52200, Türkiye
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(9), 1526; https://doi.org/10.3390/math13091526
Submission received: 27 January 2025 / Revised: 27 April 2025 / Accepted: 2 May 2025 / Published: 6 May 2025
(This article belongs to the Special Issue Submanifolds in Metric Manifolds, 2nd Edition)
Versions Notes

Abstract

In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve in terms of the Viviani’s curve. The paper is also supported by extensive graphical representations of Viviani’s curve and its Smarandache curves, as well as their respective curvatures.
Keywords: Viviani’s curve; Smarandache curves; approximation theory; ordinary least squares method Viviani’s curve; Smarandache curves; approximation theory; ordinary least squares method

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MDPI and ACS Style

Deng, Y.; Li, Y.; Şenyurt, S.; Canlı, D.; Gürler, İ. On the Special Viviani’s Curve and Its Corresponding Smarandache Curves. Mathematics 2025, 13, 1526. https://doi.org/10.3390/math13091526

AMA Style

Deng Y, Li Y, Şenyurt S, Canlı D, Gürler İ. On the Special Viviani’s Curve and Its Corresponding Smarandache Curves. Mathematics. 2025; 13(9):1526. https://doi.org/10.3390/math13091526

Chicago/Turabian Style

Deng, Yangke, Yanlin Li, Süleyman Şenyurt, Davut Canlı, and İremnur Gürler. 2025. "On the Special Viviani’s Curve and Its Corresponding Smarandache Curves" Mathematics 13, no. 9: 1526. https://doi.org/10.3390/math13091526

APA Style

Deng, Y., Li, Y., Şenyurt, S., Canlı, D., & Gürler, İ. (2025). On the Special Viviani’s Curve and Its Corresponding Smarandache Curves. Mathematics, 13(9), 1526. https://doi.org/10.3390/math13091526

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