CEVA, MENELAUS AND STEWART THEOREMS FOR GEODESIC TRIANGLES ON THE HYPERBOLIC UNIT SPHERE 2 H0

Year 2007, Volume: 2 Issue: 1, 104 - 110, 01.06.2007

Mehmet Önder

Abstract

In this study, we give Ceva, Menelaus and Stewart Theorems for geodesic triangles on the hyperbolic unit sphere 2 H0 . 

Keywords

Geodesic triangle, Lorentz space, timelike vector

H0 HİPERBOLİK BİRİM KÜRESİ ÜZERİNDEKİ GEODEZİK ÜÇGENLER İÇİN CEVA, MENELAUS VE STEWART TEOREMLERİ

Abstract

Bu çalışmada 2 H0 hiperbolik birim küresi üzerindeki geodezik üçgenler için Ceva, Menelaus ve Stewart teoremleri verilmektedir.

Keywords

Geodesic triangle, Lorentz space, timelike vector

References

• AYRES F, 1954. Theory and Problems of Plane and Spherical Trigonometry, Schaum's Outline Series, Mc-Graw-Hill Book Company.
• BELL C. AND THOMAS T.Y, 1943. Essentials of Plane and Spherical Trigonometry, Henry Hold and Company, New-York.
• BIRMAN GS. AND NOMIZO K., 1984. Trigonometry in Lorentzian Geometry, Am. Math Mont., 91, 543-549.
• BRONSTEIN IN., SEMENDJAJEV KA. MUSIOL G. AND MUHLIG H. 1995. Taschenbuch der Mathematik, Verlag Harri Deutsh, Frankfurt.
• ÖZDEMIR A. AND KAZAZ M., 2005. Hyperbolic Sine and Cosine Rules for Geodesic Triangles on the Hyperbolic Unit Ssphere 2 H0 , Mathematical and Computational Applications, Vol. 10, No. 2, pp. 193-201.
• RATCLIFFE J. G., 1994. Foundations of Hyperbolic Manifolds (Graduate Text in Mathematics), Vol.149, Springer Verlag.
• UĞURLU H. H., KAZAZ M. AND ÖZDEMİR A., 2005. Fundamental Theorems for the Hyperbolic Geodesic Triangles, Mathematical and Computational Applications, Vol. 10, No. 2, pp. 231–238.
• YAŞAYAN A. AND HEKIMOĞLU Ş., 1982. Küresel Trigonometri, K.T.Ü, Trabzon.