Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 13 Sayı: 1, 94 - 105, 30.06.2021

Öz

Kaynakça

  • [1] Bayram, E., Bilici, M., Surface family with a common involute asymptotic curve, Int. J. Geom. Methods Mod. Phys, 13(5)(2016), 1650062 (9 pages).
  • [2] Çalışkan, M., Bilici, M., Some characterizations for the pair of Involute-Evolute curves in Euclidean space, Bull. Pure Appl. Sci., 21(2)(2002), 289–294.
  • [3] Do Carmo, M.P., Differantial Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, New Jersey, 1976.
  • [4] Farouki, R.T., The approximation of non-degenerate offset surfaces, Computer Aided Geometric Design, 3(1986), 15–43.
  • [5] Gürsoy, O., Küçük, A., On the invariants of trajectory surfaces, Mech and Mach Theory, 34(4)(1999), 587–597.
  • [6] Küçük, A., On the developable of Bertrand trajectory ruled surface o sets, Intern. Math. Journal, 4(1)(2003), 57–64.
  • [7] Küçük, A., On the developable timelike trajectory ruled surfaces in Lorentz 3-space R31, App. Math. and Comp., 157(2004), 483–489.
  • [8] Laugwitz, D., Differential and Riemannian Geometry, Academic Press, New York, 1965.
  • [9] O’Neill, B., Semi-Riemannian Geometry with Application to relativity, Academic Press, New York, 1983.
  • [10] Orbay, K., Aydemir, I., The ruled surfaces generated by Frenet vectors of a curve in R31 , C.B.U. Journal of Science, 6(2)(2010), 155–160.
  • [11] Perriollat, M., Bartoli, A., A computational model of bounded developable surfaces with application to image-based three-dimensional reconstruction, Computer Animation & Virtual Worlds, 24(5) (2013) 459–476. doi:10.1002/cav.1478.
  • [12] Pottmann, H., Asperl, A., Hofer, M., Kilian, A., Architectural Geometry, Bentley Institute Press, Exton, 2007.
  • [13] Ravani, B., Ku, T.S., Bertrand offsets of ruled and developable surfaces, Comp. Aided Geom. Design, 23(2)(1991), 145–152.
  • [14] Yang, A.T., Kirson, Y., Both, B., On a kinematics theory for ruled surface, Proceedings of Fourth World Congress on the Theory of Machines and Mechanisms, Newcastle Upon Tyne, England, 1975, 737-742.
  • [15] Yaylı Y., Saracoglu, S., On developable ruled surfaces in Minkowski space, Advances in Applied Clifford Algebras, 22(2)(2012), 499-510.

On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces

Yıl 2021, Cilt: 13 Sayı: 1, 94 - 105, 30.06.2021

Öz

In this study, ruled surfaces formed by Frenet's trihedral of involute curve
$\beta $ of a given curve $\alpha $ are discussed. These surfaces are named
as involute trajectory ruled surfaces. These type of ruled surfaces are
expressed depending on the angle $\theta $ between the binormal vector $b$
and Darboux vector $D$ of the main curve (evolute) $\alpha $. Also, some new
results and theorems related to the developability of the involute
trajectory ruled surfaces are obtained. Finally we illustrate these surfaces
by presenting some examples.

Kaynakça

  • [1] Bayram, E., Bilici, M., Surface family with a common involute asymptotic curve, Int. J. Geom. Methods Mod. Phys, 13(5)(2016), 1650062 (9 pages).
  • [2] Çalışkan, M., Bilici, M., Some characterizations for the pair of Involute-Evolute curves in Euclidean space, Bull. Pure Appl. Sci., 21(2)(2002), 289–294.
  • [3] Do Carmo, M.P., Differantial Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, New Jersey, 1976.
  • [4] Farouki, R.T., The approximation of non-degenerate offset surfaces, Computer Aided Geometric Design, 3(1986), 15–43.
  • [5] Gürsoy, O., Küçük, A., On the invariants of trajectory surfaces, Mech and Mach Theory, 34(4)(1999), 587–597.
  • [6] Küçük, A., On the developable of Bertrand trajectory ruled surface o sets, Intern. Math. Journal, 4(1)(2003), 57–64.
  • [7] Küçük, A., On the developable timelike trajectory ruled surfaces in Lorentz 3-space R31, App. Math. and Comp., 157(2004), 483–489.
  • [8] Laugwitz, D., Differential and Riemannian Geometry, Academic Press, New York, 1965.
  • [9] O’Neill, B., Semi-Riemannian Geometry with Application to relativity, Academic Press, New York, 1983.
  • [10] Orbay, K., Aydemir, I., The ruled surfaces generated by Frenet vectors of a curve in R31 , C.B.U. Journal of Science, 6(2)(2010), 155–160.
  • [11] Perriollat, M., Bartoli, A., A computational model of bounded developable surfaces with application to image-based three-dimensional reconstruction, Computer Animation & Virtual Worlds, 24(5) (2013) 459–476. doi:10.1002/cav.1478.
  • [12] Pottmann, H., Asperl, A., Hofer, M., Kilian, A., Architectural Geometry, Bentley Institute Press, Exton, 2007.
  • [13] Ravani, B., Ku, T.S., Bertrand offsets of ruled and developable surfaces, Comp. Aided Geom. Design, 23(2)(1991), 145–152.
  • [14] Yang, A.T., Kirson, Y., Both, B., On a kinematics theory for ruled surface, Proceedings of Fourth World Congress on the Theory of Machines and Mechanisms, Newcastle Upon Tyne, England, 1975, 737-742.
  • [15] Yaylı Y., Saracoglu, S., On developable ruled surfaces in Minkowski space, Advances in Applied Clifford Algebras, 22(2)(2012), 499-510.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mustafa Bilici 0000-0002-3502-5027

Yayımlanma Tarihi 30 Haziran 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 13 Sayı: 1

Kaynak Göster

APA Bilici, M. (2021). On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces. Turkish Journal of Mathematics and Computer Science, 13(1), 94-105. https://doi.org/10.47000/tjmcs.803690
AMA Bilici M. On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces. TJMCS. Haziran 2021;13(1):94-105. doi:10.47000/tjmcs.803690
Chicago Bilici, Mustafa. “On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces”. Turkish Journal of Mathematics and Computer Science 13, sy. 1 (Haziran 2021): 94-105. https://doi.org/10.47000/tjmcs.803690.
EndNote Bilici M (01 Haziran 2021) On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces. Turkish Journal of Mathematics and Computer Science 13 1 94–105.
IEEE M. Bilici, “On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces”, TJMCS, c. 13, sy. 1, ss. 94–105, 2021, doi: 10.47000/tjmcs.803690.
ISNAD Bilici, Mustafa. “On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces”. Turkish Journal of Mathematics and Computer Science 13/1 (Haziran 2021), 94-105. https://doi.org/10.47000/tjmcs.803690.
JAMA Bilici M. On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces. TJMCS. 2021;13:94–105.
MLA Bilici, Mustafa. “On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces”. Turkish Journal of Mathematics and Computer Science, c. 13, sy. 1, 2021, ss. 94-105, doi:10.47000/tjmcs.803690.
Vancouver Bilici M. On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces. TJMCS. 2021;13(1):94-105.