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

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...

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Published inAIMS mathematics Vol. 9; no. 8; pp. 20136 - 20162
Main Authors Şenyurt, Süleyman, Kaya, Filiz Ertem, Canlı, Davut
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
b-pedal curve
frenet apparatus
n-pedal curve
pedal curves
smarandache curves
t-pedal curve
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024981