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© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

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.

Details

Title
On the Special Viviani’s Curve and Its Corresponding Smarandache Curves
Author
Deng Yangke 1 ; Li, Yanlin 1   VIAFID ORCID Logo  ; Şenyurt Süleyman 2   VIAFID ORCID Logo  ; Canlı Davut 2   VIAFID ORCID Logo  ; Gürler İremnur 2 

 School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China; [email protected] 
 Department of Mathematics, Ordu University, Ordu 52200, Türkiye; [email protected] (S.Ş.); [email protected] (D.C.); [email protected] (İ.G.) 
First page
1526
Publication year
2025
Publication date
2025
Publisher
MDPI AG
e-ISSN
22277390
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
3203211269
Copyright
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.