On Helices and Bertrand Curves in Euclidean 3-Space
AbstractIn this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its the tangent indicatrix and binormal indicatrix are both Bertrand curves and circular helices. Similarly, in case of a space curve is a slant helix, we demonstrate that the curve corresponding to the spherical image of its the principal normal indicatrix is both a Bertrand curve and a circular helix.
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Babaarslan, M.; Yayli, Y. On Helices and Bertrand Curves in Euclidean 3-Space. Math. Comput. Appl. 2013, 18, 1-11.
Babaarslan M, Yayli Y. On Helices and Bertrand Curves in Euclidean 3-Space. Mathematical and Computational Applications. 2013; 18(1):1-11.Chicago/Turabian Style
Babaarslan, Murat; Yayli, Yusuf. 2013. "On Helices and Bertrand Curves in Euclidean 3-Space." Math. Comput. Appl. 18, no. 1: 1-11.