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

Yangke Deng, Yanlin Li (), Süleyman Şenyurt, Davut Canlı and İremnur Gürler
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Yangke Deng: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Süleyman Şenyurt: Department of Mathematics, Ordu University, Ordu 52200, Türkiye
Davut Canlı: Department of Mathematics, Ordu University, Ordu 52200, Türkiye
İremnur Gürler: Department of Mathematics, Ordu University, Ordu 52200, Türkiye

Mathematics, 2025, vol. 13, issue 9, 1-22

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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