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

Year 2018, , 111 - 119, 30.11.2018

Tülay Erişir , Mehmet Ali Güngör

https://doi.org/10.36890/iejg.545140

Abstract

Keywords

Generalized complex plane, Cauchy-length formulas, Holditch theorem

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.