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ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE

Year 2017, Volume: 5 Issue: 2, 172 - 180, 15.10.2017

Beyhan Yılmaz Çağla Ramis Yusuf Yaylı

Abstract

This study is devoted to improve the theory of the developable ruled surfaces in terms of principal-direction curves of any spatial curve in three-dimensional Euclidean space. We obtain the new representation for developable surfaces by slant helices and the useful elements such as pitch, angle of pitch and dral with the help of a new frame $\left \{ N,C,W\right \} $. Furthermore, the investigation is observed under some special cases in terms of the director vector of surface.

Keywords

Ruled surface developable ruled surface helix slant helix

References

  • [1] A. Sarıoğlugil and A. Tutar, On ruled surfaces in euclidean space E3; Int. J. Contemp. Math. Sci., Vol. 2 (1), (2007), 1-11.
  • [2] B. Odehnal, Subdivision algorithms for ruled surfaces, Journal for Geometry and Graphics, Vol. 12 (1), (2008), 1-18.
  • [3] B. Uzunoğlu, İ. Gökk and Y. Yaylı, A new approach on curves of constant precession, Applied Mathematics and Computation, 275, (2016), 317-323.
  • [4] Ç . Ramis, B. Uzunoğlu and Y. Yaylı, New associated curves k-principle direction curves and Nk􀀀 slant helix, arXiv:1404.7369 [math.DG], 2014.
  • [5] H. H. Hacısalihoğlu, Diferensiyel Geometri, Fen Fakultesi, Ankara, 1994.
  • [6] H. H. Hacısalihoğlu, On the pitch of a closed ruled surface, Mech. and Mach. Theory, Vol. 7, (1972), 291-305.
  • [7] H. Pottmann and J. Wallner, Computational Line Geometry , Springer-Verlag, 2001.
  • [8] H. R.Muller, Uber geschlossene bewegungsvorgange , Monatsh Math. 55, (1951), 209-214.
  • [9] J. H. Choi and Y. H. Kim, Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation 218, (2012) 9116-9124.
  • [10] L.Kula and Y.Yaylı, On slant helix and its spherical indicatrix, Appl. Math. Comput. 169(1), (2005), 600-607.
  • [11] O. Gursoy, On the integral invariants of a closed ruled surface, J. Geom., Vol. 39, (1990), 80-91.
  • [12] P. Alegre , K. Arslan, A. Carriazo , C. Murathan and G. Öztürk, Some special types of developable ruled surface, Hacettepe Journal of Mathematics and Statistics, Vol. 39 (3), (2010), 319-325.
  • [13] S. Izumiya and N. Takeuchi, Special curves and ruled surfaces, Beitrage zur Algebra und Geometrie, Vol. 44 (1), (2003), 203-212.

Year 2017, Volume: 5 Issue: 2, 172 - 180, 15.10.2017

Beyhan Yılmaz Çağla Ramis Yusuf Yaylı

Abstract

References

  • [1] A. Sarıoğlugil and A. Tutar, On ruled surfaces in euclidean space E3; Int. J. Contemp. Math. Sci., Vol. 2 (1), (2007), 1-11.
  • [2] B. Odehnal, Subdivision algorithms for ruled surfaces, Journal for Geometry and Graphics, Vol. 12 (1), (2008), 1-18.
  • [3] B. Uzunoğlu, İ. Gökk and Y. Yaylı, A new approach on curves of constant precession, Applied Mathematics and Computation, 275, (2016), 317-323.
  • [4] Ç . Ramis, B. Uzunoğlu and Y. Yaylı, New associated curves k-principle direction curves and Nk􀀀 slant helix, arXiv:1404.7369 [math.DG], 2014.
  • [5] H. H. Hacısalihoğlu, Diferensiyel Geometri, Fen Fakultesi, Ankara, 1994.
  • [6] H. H. Hacısalihoğlu, On the pitch of a closed ruled surface, Mech. and Mach. Theory, Vol. 7, (1972), 291-305.
  • [7] H. Pottmann and J. Wallner, Computational Line Geometry , Springer-Verlag, 2001.
  • [8] H. R.Muller, Uber geschlossene bewegungsvorgange , Monatsh Math. 55, (1951), 209-214.
  • [9] J. H. Choi and Y. H. Kim, Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation 218, (2012) 9116-9124.
  • [10] L.Kula and Y.Yaylı, On slant helix and its spherical indicatrix, Appl. Math. Comput. 169(1), (2005), 600-607.
  • [11] O. Gursoy, On the integral invariants of a closed ruled surface, J. Geom., Vol. 39, (1990), 80-91.
  • [12] P. Alegre , K. Arslan, A. Carriazo , C. Murathan and G. Öztürk, Some special types of developable ruled surface, Hacettepe Journal of Mathematics and Statistics, Vol. 39 (3), (2010), 319-325.
  • [13] S. Izumiya and N. Takeuchi, Special curves and ruled surfaces, Beitrage zur Algebra und Geometrie, Vol. 44 (1), (2003), 203-212.
There are 13 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Beyhan Yılmaz

Çağla Ramis This is me

Yusuf Yaylı

Publication Date October 15, 2017
Submission Date October 15, 2017
Acceptance Date May 31, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Yılmaz, B., Ramis, Ç., & Yaylı, Y. (2017). ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE. Konuralp Journal of Mathematics, 5(2), 172-180.
AMA Yılmaz B, Ramis Ç, Yaylı Y. ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE. Konuralp J. Math. October 2017;5(2):172-180.
Chicago Yılmaz, Beyhan, Çağla Ramis, and Yusuf Yaylı. “ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE”. Konuralp Journal of Mathematics 5, no. 2 (October 2017): 172-80.
EndNote Yılmaz B, Ramis Ç, Yaylı Y (October 1, 2017) ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE. Konuralp Journal of Mathematics 5 2 172–180.
IEEE B. Yılmaz, Ç. Ramis, and Y. Yaylı, “ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE”, Konuralp J. Math., vol. 5, no. 2, pp. 172–180, 2017.
ISNAD Yılmaz, Beyhan et al. “ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE”. Konuralp Journal of Mathematics 5/2 (October 2017), 172-180.
JAMA Yılmaz B, Ramis Ç, Yaylı Y. ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE. Konuralp J. Math. 2017;5:172–180.
MLA Yılmaz, Beyhan et al. “ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE”. Konuralp Journal of Mathematics, vol. 5, no. 2, 2017, pp. 172-80.
Vancouver Yılmaz B, Ramis Ç, Yaylı Y. ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE. Konuralp J. Math. 2017;5(2):172-80.
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