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

Ö. Gökmen Yıldız; Sıddıka Ö. Karakuş; H. Hilmi Hacısalihoğlu

doi:10.36890/iejg.591892

Research Article

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

Year 2016, Volume: 9 Issue: 1, 62 - 69, 30.04.2016

Ö. Gökmen Yıldız Sıddıka Ö. Karakuş H. Hilmi Hacısalihoğlu

https://doi.org/10.36890/iejg.591892

Abstract

Keywords

Ruled Surface, Developable Surface, Dual Lorentzian Unit Sphere, Minkowski Space

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, Volume: 9 Issue: 1, 62 - 69, 30.04.2016

Ö. Gökmen Yıldız Sıddıka Ö. Karakuş H. Hilmi Hacısalihoğlu

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 Volume: 9 Issue: 1

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.