Research Article
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Directional Bertrand Curves

Year 2018, Volume: 31 Issue: 1, 202 - 211, 01.03.2018

Mustafa Dede , Cumali Ekici

https://izlik.org/JA32NS42HZ

Abstract

It is well known that a characteristic property of the Bertrand curve is

the existence of a linear relation between its curvature and torsion. In this

paper, we propose a new method for generating Bertrand curves, which

avoids the basic restrictions. Our main result is that every space curve is

a directional Bertrand curve with in nite directional Bertrand mates.

Keywords

Bertrand Curves offset Frenet frame

References

  • 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.

Year 2018, Volume: 31 Issue: 1, 202 - 211, 01.03.2018

Mustafa Dede , Cumali Ekici

https://izlik.org/JA32NS42HZ

Abstract

References

  • 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.
There are 3 citations in total.

Details

Journal Section Research Article
Authors

Mustafa Dede

Cumali Ekici

Publication Date March 1, 2018
IZ https://izlik.org/JA32NS42HZ
Published in Issue Year 2018 Volume: 31 Issue: 1

Cite

APA Dede, M., & Ekici, C. (2018). Directional Bertrand Curves. Gazi University Journal of Science, 31(1), 202-211. https://izlik.org/JA32NS42HZ
AMA 1.Dede M, Ekici C. Directional Bertrand Curves. Gazi University Journal of Science. 2018;31(1):202-211. https://izlik.org/JA32NS42HZ
Chicago Dede, Mustafa, and Cumali Ekici. 2018. “Directional Bertrand Curves”. Gazi University Journal of Science 31 (1): 202-11. https://izlik.org/JA32NS42HZ.
EndNote Dede M, Ekici C (March 1, 2018) Directional Bertrand Curves. Gazi University Journal of Science 31 1 202–211.
IEEE [1]M. Dede and C. Ekici, “Directional Bertrand Curves”, Gazi University Journal of Science, vol. 31, no. 1, pp. 202–211, Mar. 2018, [Online]. Available: https://izlik.org/JA32NS42HZ
ISNAD Dede, Mustafa - Ekici, Cumali. “Directional Bertrand Curves”. Gazi University Journal of Science 31/1 (March 1, 2018): 202-211. https://izlik.org/JA32NS42HZ.
JAMA 1.Dede M, Ekici C. Directional Bertrand Curves. Gazi University Journal of Science. 2018;31:202–211.
MLA Dede, Mustafa, and Cumali Ekici. “Directional Bertrand Curves”. Gazi University Journal of Science, vol. 31, no. 1, Mar. 2018, pp. 202-11, https://izlik.org/JA32NS42HZ.
Vancouver 1.Mustafa Dede, Cumali Ekici. Directional Bertrand Curves. Gazi University Journal of Science [Internet]. 2018 Mar. 1;31(1):202-11. Available from: https://izlik.org/JA32NS42HZ