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Research Article | Open Access

Pedal curves obtained from Frenet vector of a space curve and Smarandache curves belonging to these curves

Süleyman Şenyurt1( ), Filiz Ertem Kaya2, Davut Canlı1
Department of Mathematics, Ordu University, Ordu, 52200, Türkiye
Department of Mathematics, Niğde Ömer Halisdemir University, Niğde, 51240, Türkiye
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Abstract

In this study, first the pedal curves as the geometric locus of perpendicular projections to the Frenet vectors of a space curve were defined and the Frenet vectors, curvature, and torsion of these pedal curves were calculated. Second, for each pedal curve, Smarandache curves were defined by taking the Frenet vectors as position vectors. Finally, the expressions of Frenet vectors, curvature, and torsion related to the main curves were obtained for each Smarandache curve. Thus, new curves were added to the curve family.

Keywords

pedal curvesFrenet apparatusT-pedal curveN-pedal curveB-pedal curveSmarandache curves
CLC number: 53A04

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 20136-20162
DOI: 10.3934/math.2024981

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Cite this article:
Şenyurt S, Kaya FE, Canlı D. Pedal curves obtained from Frenet vector of a space curve and Smarandache curves belonging to these curves. AIMS Mathematics, 2024, 9(8): 20136-20162. https://doi.org/10.3934/math.2024981

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Received: 02 May 2024
Revised: 05 June 2024
Accepted: 13 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)