Dergiler / Konuralp Journal of Mathematics / 2015 / Cilt: 3 - Sayı: 1

ON THE DETERMINATION OF A DEVELOPABLE SPHERICAL ORTHOTOMIC TIMELIKE RULED SURFACE

Sayfa
75–83
Yayın Tarihi
2015-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The paper concludes with an example related to this method.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, a method for determination of developable spherical orthotomic ruled surfaces generated by a spacelike curve on dual hyperbolic unit sphere is given by using dual vector calculus in R31 .
📊
Temel Bulgular & Veri:We show that dual vectorial expression of a developable spherical orthotomic timelike ruled surface can be obtained from coordinates and the rst derivatives of the base curve.
💡
Sonuç & Katkı:The paper concludes with an example related to this method.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ruled Surface · Developable Surface · Dual Hyperbolic Unit Sphere

Abstract

In this paper, a method for determination of developable spherical orthotomic ruled surfaces generated by a spacelike curve on dual hyperbolic unit sphere is given by using dual vector calculus in R31 . We show that dual vectorial expression of a developable spherical orthotomic timelike ruled surface can be obtained from coordinates and the rst derivatives of the base curve. The paper concludes with an example related to this method.

🔖

Bu Makaleye Atıf Yap

YILDIZ, Ö. G., KARAKUŞ, S. Ö., HACISALİHOĞLU, H. H. (2015). ON THE DETERMINATION OF A DEVELOPABLE SPHERICAL ORTHOTOMIC TIMELIKE RULED SURFACE. Konuralp Journal of Mathematics, Cilt: 3 - Sayı: 1, 75–83. https://ajindex.com/articles/786744

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. N. Alamo, C. Criado, Generalized Antiorthotomics and their Singularities, Inverse Problems, 18(3)(2002), 881-889
  2. W. Blaschke, Vorlesungen Uber Di erential Geometry I., Verlag von Julieus Springer in Berlin (1930) pp.89
  3. J. W. Bruce, On Singularities, Envelopes and Elementary Di erential Geometry, Math. Proc. Cambridge Philos. Soc., 89 (1) (1981) 43-48
  4. J. W. Bruce, P. J. Giblin, Curves and Singularities. A Geometrical Introduction to Singularity Theory, Second Edition, University Press, Cambridge, (1992)
  5. J. W. Bruce, P. J. Giblin, One-parameter Families of Caustics by Re exion in the Plane, Quart. J. Math. Oxford Ser., (2), 35(139) (1984) 243-251
  6. C. Georgiou, T. Hasanis, D. Koutrou otis, On the Caustic of a Convex Mirror, Geom. Ded- icata, 28(2)(1988), 153-169
  7. C. G. Gibson, Elementary Geometry of Di erentiable Curves, Cambridge University Press, May (2011)
  8. J. Hoschek, Smoothing of curves and surfaces. Computer Aided Geometric Design, Vol. 2, No. 1-3 (1985), special issue, 97-105. [9]  O. G. Yldz, H. H. Hacsaligoglu, Study Map of Orthotomic of a Circle, International J. Math. Combin., Vol.4 (2014), 07-17. [10]  O. G. Yldz, S.  O. Karakus, H. H. Hacsaligoglu,On the determination of a developable spherical orthotomic ruled surface, Bull. Math. Sci., (2014) Doi: 10.1007/s13373-014-0063-5. [11]  O. Kose, A Method of the Determination of a Developable Ruled Surface, Mechanism and Machine Theory, 34 (1999), 1187-1193
  9. C.Ekici, E. Ozusaglam, On the Method of Determination of a Developable Timelike Ruled Surface, Kuwait Journal of Science and Engineering, Vol:39(1A), 19-41, 2012
  10. C.Y. Li, R.H. Wang, C.G. Zhu, An approach for designing a developable surface through a given line of curvature, Computer Aided Design, 45 (2013), 621-627
  11. J.M. McCarthy, On The Scalar and Dual Formulations of the Curvature Theory of Line Trajectories, ASME Journal of Mechanisms, Transmissions and Automation in Design, (1987), 109/101
  12. E. Study, Geometrie der Dynamen, Leibzig, (1903)
  13. H. H. Ugurlu, A. C aliskan, The Study mapping for directed spacelike and timelike lines in Minkowski 3-space, Mathematical and Computational Applications, Vol. 1, No:2 (1996), 142-148
  14. G. R. Veldkamp, On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics, Mech. Mach. Theory, 11 (1976), no. 2, 141-156
  15. J.F. Xiong, Spherical Orthotomic and Spherical Antiorthotomic, Acta Mathematica Sinica