Mustafa Dede, Cumali Ekici

98114

Directional Bertrand Curves

It is well known that a characteristic property of the Bertrand curve isthe existence of a linear relation between its curvature and torsion. In thispaper, we propose a new method for generating Bertrand curves, whichavoids the basic restrictions. Our main result is that every space curve isa directional Bertrand curve with innite directional Bertrand mates.
Keywords:

Bertrand Curves, , offset , Frenet frame,

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  • Bloomenthal, J. 1990. Calculation of reference frames along a space curve. Graphics Gems, 1: 567-571.
  • Choi, J.H., Kang, T.H. & Kim, Y.H. 2012. Bertrand curves in 3- dimensional space forms. Applied Mathematics and Computation, 219: 1040-1046.
  • Ekmekci, N. & Ilarslan, K. 2001. On Bertrand curves and their characterization. Di fferential Geometry Dynamical System, 3: 17-24.
Gazi University Journal of Science-Cover
  • Yayın Aralığı: 4
  • Başlangıç: 1988
  • Yayıncı: Gazi Üniversitesi, Fen Bilimleri Enstitüsü
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