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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yangke Deng & Yanlin Li & Süleyman Şenyurt & Davut Canlı & İremnur Gürler, 2025. "On the Special Viviani’s Curve and Its Corresponding Smarandache Curves," Mathematics, MDPI, vol. 13(9), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1526-:d:1650040
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