Affiliation:
1. KILIS 7 ARALIK UNIVERSITY
Abstract
The first and second derivatives of a curve provide us fundamental
information in the study of the behavior of curve near a point. However,
if a curve is a polynomial space curve of degree n, we don’t know what
is the geometric meaning of the n-th derivative of the curve? There is no
doubt that the Frenet frame is not suitable for this purpose because it is
constructed by using first and second derivatives of a curve. On the other
hand, in this paper by using a new frame called as Flc-frame we are able
to give the geometric meaning of the n-th derivative of a curve. Moreover,
we explore some basic concepts regarding polynomial space curves from
point of view of Flc-frame in three dimensional Euclidean space.
Publisher
Turkish Journal of Mathematics and Computer Science, Association of Mathematicians
Reference14 articles.
1. Ayvacı, K.H., Senyurt, S., Canlı, D., Some characterizations of spherical indicatrix curves generated by Flc frame, Turk. J. Math. Comput. Sci., 13(2021), 379–387.
2. Bishop, R.L., There is more than one way to frame a curve, Amer. Math. Monthly, 82(1975), 246–251.
3. Dede, M., A new representation of tubular surfaces, Houston Journal of Mathematics, 45(2018), 707–720.
4. Dede, M., Ekici, C., Görgülü, A., Directional q-frame along a space curve, IJARCSSE, 5(2015), 775–780.
5. Farouki, R. T., Pythagorean-Hodograph Curves: Algebra and Geometry, Springer, 2008.