Dergiler / International Electronic Journal of Geometry / 2016 / Cilt: 9 - Sayı: 1

A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R3

Sayfa
62–69
Yayın Tarihi
2022-10-18
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 paperconcludes 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 is1given by using dual vector calculus inR3spherical orthotomic spacelike and timelike ruled surface generated by a curve on dual Lorentzianunit sphere can be obtained from coordinates and the first derivatives of the base curve.
📊
Temel Bulgular & Veri:In this paper, a method for determination of developable spherical orthotomic ruled surfaces is1given by using dual vector calculus inR3spherical orthotomic spacelike and timelike ruled surface generated by a curve on dual Lorentzianunit sphere can be obtained from coordinates and the first derivatives of the base curve.
💡
Sonuç & Katkı:The paperconcludes with an example related to this method
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, a method for determination of developable spherical orthotomic ruled surfaces is1given by using dual vector calculus inR3spherical orthotomic spacelike and timelike ruled surface generated by a curve on dual Lorentzianunit sphere can be obtained from coordinates and the first derivatives of the base curve. The paperconcludes with an example related to this method

🔖

Bu Makaleye Atıf Yap

YILDIZ, Ö. G., KARAKUS, S. Ö., HACAISALİHOĞLU, H. H. (2022). A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R3. International Electronic Journal of Geometry, Cilt: 9 - Sayı: 1, 62–69. https://ajindex.com/articles/539710

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. Alamo, N. and Criado, C., Generalized Antiorthotomics and their Singularities, Inverse Problems, 18(3) (2002), 881-889.
  2. Blaschke, W., Vorlesungen Über Differential Geometry I., Verlag von Julieus Springer, Berlin 1930.
  3. Bruce, J. W., On Singularities, Envelopes and Elementary Differential Geometry, Math. Proc. Cambridge Philos. Soc., 89 (1) (1981), 43-48.
  4. Bruce, J. W. and Giblin, P. J., Curves and Singularities. A Geometrical Introduction to Singularity Theory, Second Edition,
  5. University Press, Cambridge, (1992).
  6. Bruce, J. W. and Giblin, P. J., One-parameter Families of Caustics by Reflexion in the Plane, Quart. J. Math. Oxford Ser., (2), 35 (139) (1984), 251. Georgiou, C., Hasanis, T. and Koutroufiotis, D., On the Caustic of a Convex Mirror, Geom. Dedicata, 28 (2) (1988), 153-169.
  7. Gibson, C. G., Elementary Geometry of Differentiable Curves, Cambridge University Press, 2011.
  8. Hoschek, J., Smoothing of curves and surfaces, Computer Aided Geometric Design, Vol. 2, No. 1-3 (1985), special issue, 97-105.
  9. Köse, Ö., A Method of the Determination of a Developable Ruled Surface, Mechanism and Machine Theory, 34 (1999), 1187-1193.
  10. Li, C.Y., Wang, R.H. and Zhu, C.G., An approach for designing a developable surface through a given line of curvature, Computer Aided Design, 45 (2013), 621-627.
  11. McCarthy, J.M., 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. Study, E., Geometrie der Dynamen, Leibzig, 1903. U ?gurlu, H. H. and Çali¸skan, A., The Study mapping for directed spacelike and timelike lines in Minkowski 3-space, Mathematical and Computational Applications, Vol. 1, No:2 (1996), 142-148.
  13. Veldkamp, G. R., On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics, Mech. Mach. Theory, 11 (1976), no. 2, 141-156.
  14. Xiong, J.F., Spherical Orthotomic and Spherical Antiorthotomic, Acta Mathematica Sinica, 23 (2007), Issue 9, 1673-1682.
  15. Yaylı, Y., Çalı¸skan, A., and U ?gurlu, H.H., The E. Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit SpheresH2andS2, Mathematical Proceedings of the Royal Irish Academy, 102A (2002), 1, 37-47.
  16. Yıldız, Ö. G., Hacısaliho ?glu, H.H., Study Map of Spherical Orthotomic of a Circle, International J. Math. Combin, Vol.4, (2014), 07-17.
  17. Yıldız, Ö. G., Karaku¸s, S. Ö., Hacısaliho ?glu, H.H., On the determination of a developable spherical orthotomic ruled surface, Bull. Math. Sci., (2014) 5:137-1