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Math. Comput. Appl. 2013, 18(1), 1-11; doi:10.3390/mca18010001

On Helices and Bertrand Curves in Euclidean 3-Space

1
Department of Mathematics, Faculty of Arts and Sciences Bozok University, Yozgat, Turkey
2
Department of Mathematics, Faculty of Science Ankara University, Tandogan, Ankara, Turkey
*
Authors to whom correspondence should be addressed.
Published: 1 April 2013
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Abstract

In 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.
Keywords: Helix; Bertrand curve; Sabban frame; Spherical images Helix; Bertrand curve; Sabban frame; Spherical images
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Babaarslan, M.; Yayli, Y. On Helices and Bertrand Curves in Euclidean 3-Space. Math. Comput. Appl. 2013, 18, 1-11.

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