Yazar "Kocayigit, Huseyin" seçeneğine göre listele

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    AN EXPLICIT CHARACTERIZATION OF SPHERICAL CURVES ACCORDING TO BISHOP FRAME AND AN APPROXIMATELY SOLUTION
    (Vinca Inst Nuclear Sci, 2019) Balki Okullu, Pinar; Kocayigit, Huseyin; Agirman Aydin, Tuba
    In this paper, spherical curves are studied by using Bishop frame. First, the differential equation characterizing the spherical curves is given. Then, we exhibit that the position vector of a curve which is lying on a sphere satisfies a third-order linear differential equation. Then we solve this linear differential equation by using Bernstein series solution method.
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    Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold
    (Walter De Gruyter Gmbh, 2021) Aydin, Tuba Agirman; Sezer, Mehmet; Kocayigit, Huseyin
    In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.
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    Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width
    (Walter De Gruyter Gmbh, 2021) Aydin, Tuba Agirman; Ayazoglu, Rabil; Kocayigit, Huseyin
    The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach. The geometric properties of this curve type are examined with the help of these solutions.
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    New moving frames for the curves lying on a surface
    (Yildiz Technical Univ, 2024) Alkan, Akin; Kocayigit, Huseyin; Agirman Aydin, Tuba
    In this article, three new orthogonal frames are defined for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called Osculator Darboux Frame, Normal Darboux Frame and Rectifying Darboux Frame, respectively. Also, the Osculator Darboux Frame components and curvatures are calculated for a presented example.
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    TIMELIKE HELICES IN THE SEMI-EUCLIDEAN SPACE E24
    (Honam Mathematical Soc, 2022) Aydin, Tuba Agirman; Ayazoglu, Rabil; Kocayigit, Huseyin
    In this paper, we define timelike curves in R-2(4) and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R-2(4), taking into account their curvatures. In addition, we study timelike slant helices, timelike B-1-slant helices, timelike B-2-slant helices in four dimensional semi-Euclidean space, R-2(4). And then we obtain an approximate solution for the timelike B-1 slant helix with Taylor matrix collocation method.