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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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    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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    A SPECIAL INTERPRETATION OF THE CONCEPT CONSTANT BREADTH FOR A SPACE CURVE
    (Vinca Inst Nuclear Sci, 2019) Agirman Aydin, Tuba
    The definition of curve of constant breadth in the literature is made by using tangent vectors, which are parallel and opposite directions, at opposite points of the curve. In this study, normal vectors of the curve, which are parallel and opposite directions are placed at the exit point of the concept of curve of constant breadth. In this study, on the concept of curve of constant breadth according to normal vector is worked. At the conclusion of the study, is obtained a system of linear differential equations with variable coefficients characterizing space curves of constant breadth according to normal vector. The coefficients of this system of equations are functions depend on the curvature and torsion of the curve. Then is obtained an approximate solution of this system by using the Taylor matrix collocation method. In summary, in this study, a different interpretation is made for the concept of space curve of constant breadth, the first time. Then this interpretation is used to obtain a characterization. As a result, this characterization we 've obtained is solved.