Research Article
Year 2018,
Volume: 31 Issue: 1, 202 - 211, 01.03.2018
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
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
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 | Mathematics |
|---|---|
| Authors | |
| Publication Date | March 1, 2018 |
| Published in Issue | Year 2018 Volume: 31 Issue: 1 |