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    Pedal curves obtained from Frenet vector of a space curve and Smarandache curves belonging to these curves
    (Amer Inst Mathematical Sciences-Aims, 2024) Senyurt, Suleyman; Kaya, Filiz Ertem; Canli, Davut
    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.
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    The Pedal Curves Generated by Alternative Frame Vectors and Their Smarandache Curves
    (Mdpi, 2024) Canli, Davut; Senyurt, Suleyman; Kaya, Filiz Ertem; Grilli, Luca
    In this paper, pedal-like curves are defined resulting from the orthogonal projection of a fixed point on the alternative frame vectors of a given regular curve. For each pedal curve, the Frenet vectors, the curvature and the torsion functions are found to provide the common relations among the main curve and its pedal curves. Then, Smarandache curves are defined by using the alternative frame vectors of each pedal curve as position vectors. The relations of the Frenet apparatus are also established for the pedal curves and their corresponding Smarandache curves. Finally, the expressions of the alternative frame apparatus of each Smarandache curves are given in terms of the alternative frame elements of the pedal curves. Thus, a set of new symmetric curves are introduced that contribute to the vast curve family.