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

Yıl 2018, Cilt: 11 Sayı: 2, 111 - 119, 30.11.2018
https://doi.org/10.36890/iejg.545140

Öz

Kaynakça

  • [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.
Yıl 2018, Cilt: 11 Sayı: 2, 111 - 119, 30.11.2018
https://doi.org/10.36890/iejg.545140

Öz

Kaynakça

  • [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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Tülay Erişir

Mehmet Ali Güngör

Yayımlanma Tarihi 30 Kasım 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 11 Sayı: 2

Kaynak Göster

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. Kasım 2018;11(2):111-119. doi:10.36890/iejg.545140
Chicago Erişir, Tülay, ve Mehmet Ali Güngör. “The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p”. International Electronic Journal of Geometry 11, sy. 2 (Kasım 2018): 111-19. https://doi.org/10.36890/iejg.545140.
EndNote Erişir T, Güngör MA (01 Kasım 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 ve M. A. Güngör, “The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p”, Int. Electron. J. Geom., c. 11, sy. 2, ss. 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 (Kasım 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 ve Mehmet Ali Güngör. “The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p”. International Electronic Journal of Geometry, c. 11, sy. 2, 2018, ss. 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.