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A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3)

Year 2016, , 62 - 69, 30.04.2016
https://doi.org/10.36890/iejg.591892

Abstract


References

  • [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, University Press, Cambridge, (1992).
  • [5] 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), 243-251.
  • [6] 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.
  • [13] Uğurlu, H. H. and Çaliskan, 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.
  • [14] 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.
  • [15] Xiong, J.F., Spherical Orthotomic and Spherical Antiorthotomic, Acta Mathematica Sinica, 23 (2007), Issue 9, 1673-1682.
  • [16] Yaylı, Y., Çalışkan, A., and Uğurlu, H.H., The E. Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit Spheres H^2_0 and S^2_1 Mathematical Proceedings of the Royal Irish Academy, 102A (2002), 1, 37-47.
  • [17] Yıldız, Ö. G., Hacısalihogğlu, H.H., Study Map of Spherical Orthotomic of a Circle, International J. Math. Combin, Vol.4, (2014), 07-17.
  • [18] Yıldız, Ö. G., Karakus¸, S. Ö., Hacısalihoğlu, H.H., On the determination of a developable spherical orthotomic ruled surface, Bull. Math. Sci., (2014) 5:137-146.
  • [19] Yıldız, Ö. G., Karakus¸, S. Ö., Hacısalihogğlu, H.H., On the Determination of a Timelike Developable Spherical Orthotomic RuledSurface,Konuralp Journal of Mathematic, Volume 3 No. 1 (2015) 75-83.
Year 2016, , 62 - 69, 30.04.2016
https://doi.org/10.36890/iejg.591892

Abstract

References

  • [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, University Press, Cambridge, (1992).
  • [5] 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), 243-251.
  • [6] 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.
  • [13] Uğurlu, H. H. and Çaliskan, 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.
  • [14] 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.
  • [15] Xiong, J.F., Spherical Orthotomic and Spherical Antiorthotomic, Acta Mathematica Sinica, 23 (2007), Issue 9, 1673-1682.
  • [16] Yaylı, Y., Çalışkan, A., and Uğurlu, H.H., The E. Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit Spheres H^2_0 and S^2_1 Mathematical Proceedings of the Royal Irish Academy, 102A (2002), 1, 37-47.
  • [17] Yıldız, Ö. G., Hacısalihogğlu, H.H., Study Map of Spherical Orthotomic of a Circle, International J. Math. Combin, Vol.4, (2014), 07-17.
  • [18] Yıldız, Ö. G., Karakus¸, S. Ö., Hacısalihoğlu, H.H., On the determination of a developable spherical orthotomic ruled surface, Bull. Math. Sci., (2014) 5:137-146.
  • [19] Yıldız, Ö. G., Karakus¸, S. Ö., Hacısalihogğlu, H.H., On the Determination of a Timelike Developable Spherical Orthotomic RuledSurface,Konuralp Journal of Mathematic, Volume 3 No. 1 (2015) 75-83.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ö. Gökmen Yıldız

Sıddıka Ö. Karakuş

H. Hilmi Hacısalihoğlu This is me

Publication Date April 30, 2016
Published in Issue Year 2016

Cite

APA Yıldız, Ö. G., Karakuş, S. Ö., & Hacısalihoğlu, H. H. (2016). A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3). International Electronic Journal of Geometry, 9(1), 62-69. https://doi.org/10.36890/iejg.591892
AMA Yıldız ÖG, Karakuş SÖ, Hacısalihoğlu HH. A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3). Int. Electron. J. Geom. April 2016;9(1):62-69. doi:10.36890/iejg.591892
Chicago Yıldız, Ö. Gökmen, Sıddıka Ö. Karakuş, and H. Hilmi Hacısalihoğlu. “A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3)”. International Electronic Journal of Geometry 9, no. 1 (April 2016): 62-69. https://doi.org/10.36890/iejg.591892.
EndNote Yıldız ÖG, Karakuş SÖ, Hacısalihoğlu HH (April 1, 2016) A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3). International Electronic Journal of Geometry 9 1 62–69.
IEEE Ö. G. Yıldız, S. Ö. Karakuş, and H. H. Hacısalihoğlu, “A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3)”, Int. Electron. J. Geom., vol. 9, no. 1, pp. 62–69, 2016, doi: 10.36890/iejg.591892.
ISNAD Yıldız, Ö. Gökmen et al. “A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3)”. International Electronic Journal of Geometry 9/1 (April 2016), 62-69. https://doi.org/10.36890/iejg.591892.
JAMA Yıldız ÖG, Karakuş SÖ, Hacısalihoğlu HH. A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3). Int. Electron. J. Geom. 2016;9:62–69.
MLA Yıldız, Ö. Gökmen et al. “A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3)”. International Electronic Journal of Geometry, vol. 9, no. 1, 2016, pp. 62-69, doi:10.36890/iejg.591892.
Vancouver Yıldız ÖG, Karakuş SÖ, Hacısalihoğlu HH. A New Approach about the Determination of a Developable Spherical Orthotomic Ruled Surface in R(1,3). Int. Electron. J. Geom. 2016;9(1):62-9.