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The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p

Year 2018, Volume: 11 Issue: 2, 111 - 119, 30.11.2018
https://doi.org/10.36890/iejg.545140

Abstract

References

  • [1] (Bayrak) Gürses, N., Yüce, S., One-Parameter Planar Motions in Generalized Complex Number Plane Cj . Adv. Appl. Clifford Algebr. 4 (2015), no.25, 889-903.
  • [2] (Bayrak) Gürses, N., Yüce, S., One-Parameter Planar Motions in Affine Cayley-Klein Planes. European Journal of Pure and Applied Mathematics 7 (2014), no.3, 335-342.
  • [3] Blaschke W., Müller, H.R., Ebene Kinematik. Verlag Oldenbourg, München, 1956.
  • [4] A. P. CLIFFORD, The Math Book: 250 Milestones in the History of Mathematics. Sterling, ISBN 978-1-4027-5796-9, 2009.
  • [5] Erişir, T., Güngör, M.A., Tosun, M., A New Generalization of the Steiner Formula and the Holditch Theorem. Adv. Appl. Clifford Algebr. 26 (2016), no.1, 97-113.
  • [6] Erişir, T., Güngör, M.A., Tosun, M., The Holditch-Type Theorem for the Polar Moment of Inertia of the Orbit Curve in the Generalized Complex Plane. Adv. Appl. Clifford Algebr. 26 (2016), no.4, 1179-1193.
  • [7] Hacısalihoğlu, H. Hilmi., On the Geometry of Motion of Lorentzian Plane. Proc. of Assiut First International Conference of Mathematics and Statistics, Part I, University of Assiut, Assiut, Egypt, (1990), 87-107.
  • [8] Harkin, A.A., Harkin, J.B., Geometry of Generalized Complex Numbers. Math. Mag. 77 (2004), no.2, 118-129.
  • [9] Hering, L., Sätze vom Holditch-Typ für ebene Kurven. Elem. Math. 38 (1983), 39-49.
  • [10] Holditch, H., Geometrical Theorem. Q. J. Pure Appl. Math. 2 (1858), 38.
  • [11] Klein, F., Über die sogenante nicht-Euklidische Geometrie. Gesammelte Mathematische Abhandlungen (1921), 254-305.
  • [12] Klein, F., Vorlesungen über nicht-Euklidische Geometrie. Springer, Berlin, 1928.
  • [13] Potmann, H., Holditch-Sicheln. Arc. Math. 44 (1985), 373-378.
  • [14] Potmann, H., Zum Satz von Holditch in der Euklidischen Ebene. Elem. Math. 41 (1986), 1-6.
  • [15] Sachs, H., Ebene Isotrope Geometrie. Fiedr. Vieweg-Sohn, 1987.
  • [16] Spivak, M., Calculus on Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus.W. A. Benjamin, New York, 1965.
  • [17] Steiner, J., Gesammelte Werke II. De Gruyter Verlag, Berlin, 1882.
  • [18] Yaglom, I.M., Complex Numbers in Geometry. Academic, Press, New York, 1968.
  • [19] Yaglom, I.M., A Simple non-Euclidean Geometry and its Physical Basis. Springer-Verlag, New-York, 1979.
  • [20] Yüce, S., Kuruoğlu, N., Cauchy Formulas for Enveloping Curves in the Lorentzian Plane and Lorentzian Kinematics. Result. Math. 54 (2009), 199-206.
Year 2018, Volume: 11 Issue: 2, 111 - 119, 30.11.2018
https://doi.org/10.36890/iejg.545140

Abstract

References

  • [1] (Bayrak) Gürses, N., Yüce, S., One-Parameter Planar Motions in Generalized Complex Number Plane Cj . Adv. Appl. Clifford Algebr. 4 (2015), no.25, 889-903.
  • [2] (Bayrak) Gürses, N., Yüce, S., One-Parameter Planar Motions in Affine Cayley-Klein Planes. European Journal of Pure and Applied Mathematics 7 (2014), no.3, 335-342.
  • [3] Blaschke W., Müller, H.R., Ebene Kinematik. Verlag Oldenbourg, München, 1956.
  • [4] A. P. CLIFFORD, The Math Book: 250 Milestones in the History of Mathematics. Sterling, ISBN 978-1-4027-5796-9, 2009.
  • [5] Erişir, T., Güngör, M.A., Tosun, M., A New Generalization of the Steiner Formula and the Holditch Theorem. Adv. Appl. Clifford Algebr. 26 (2016), no.1, 97-113.
  • [6] Erişir, T., Güngör, M.A., Tosun, M., The Holditch-Type Theorem for the Polar Moment of Inertia of the Orbit Curve in the Generalized Complex Plane. Adv. Appl. Clifford Algebr. 26 (2016), no.4, 1179-1193.
  • [7] Hacısalihoğlu, H. Hilmi., On the Geometry of Motion of Lorentzian Plane. Proc. of Assiut First International Conference of Mathematics and Statistics, Part I, University of Assiut, Assiut, Egypt, (1990), 87-107.
  • [8] Harkin, A.A., Harkin, J.B., Geometry of Generalized Complex Numbers. Math. Mag. 77 (2004), no.2, 118-129.
  • [9] Hering, L., Sätze vom Holditch-Typ für ebene Kurven. Elem. Math. 38 (1983), 39-49.
  • [10] Holditch, H., Geometrical Theorem. Q. J. Pure Appl. Math. 2 (1858), 38.
  • [11] Klein, F., Über die sogenante nicht-Euklidische Geometrie. Gesammelte Mathematische Abhandlungen (1921), 254-305.
  • [12] Klein, F., Vorlesungen über nicht-Euklidische Geometrie. Springer, Berlin, 1928.
  • [13] Potmann, H., Holditch-Sicheln. Arc. Math. 44 (1985), 373-378.
  • [14] Potmann, H., Zum Satz von Holditch in der Euklidischen Ebene. Elem. Math. 41 (1986), 1-6.
  • [15] Sachs, H., Ebene Isotrope Geometrie. Fiedr. Vieweg-Sohn, 1987.
  • [16] Spivak, M., Calculus on Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus.W. A. Benjamin, New York, 1965.
  • [17] Steiner, J., Gesammelte Werke II. De Gruyter Verlag, Berlin, 1882.
  • [18] Yaglom, I.M., Complex Numbers in Geometry. Academic, Press, New York, 1968.
  • [19] Yaglom, I.M., A Simple non-Euclidean Geometry and its Physical Basis. Springer-Verlag, New-York, 1979.
  • [20] Yüce, S., Kuruoğlu, N., Cauchy Formulas for Enveloping Curves in the Lorentzian Plane and Lorentzian Kinematics. Result. Math. 54 (2009), 199-206.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Tülay Erişir

Mehmet Ali Güngör

Publication Date November 30, 2018
Published in Issue Year 2018 Volume: 11 Issue: 2

Cite

APA Erişir, T., & Güngör, M. A. (2018). The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p. International Electronic Journal of Geometry, 11(2), 111-119. https://doi.org/10.36890/iejg.545140
AMA Erişir T, Güngör MA. The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p. Int. Electron. J. Geom. November 2018;11(2):111-119. doi:10.36890/iejg.545140
Chicago Erişir, Tülay, and Mehmet Ali Güngör. “The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p”. International Electronic Journal of Geometry 11, no. 2 (November 2018): 111-19. https://doi.org/10.36890/iejg.545140.
EndNote Erişir T, Güngör MA (November 1, 2018) The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p. International Electronic Journal of Geometry 11 2 111–119.
IEEE T. Erişir and M. A. Güngör, “The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p”, Int. Electron. J. Geom., vol. 11, no. 2, pp. 111–119, 2018, doi: 10.36890/iejg.545140.
ISNAD Erişir, Tülay - Güngör, Mehmet Ali. “The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p”. International Electronic Journal of Geometry 11/2 (November 2018), 111-119. https://doi.org/10.36890/iejg.545140.
JAMA Erişir T, Güngör MA. The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p. Int. Electron. J. Geom. 2018;11:111–119.
MLA Erişir, Tülay and Mehmet Ali Güngör. “The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p”. International Electronic Journal of Geometry, vol. 11, no. 2, 2018, pp. 111-9, doi:10.36890/iejg.545140.
Vancouver Erişir T, Güngör MA. The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p. Int. Electron. J. Geom. 2018;11(2):111-9.