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Math. Comput. Appl. 2005, 10(2), 203-209; doi:10.3390/mca10020203

Hyperbolic Sine and Cosine Rules for Geodesic Triangles on the Hyperbolic Unit Sphere \(H_{0}^{2}\)

Department of Mathematics, Celal Bayar University, Muradiye Campus, 45047, Manisa, Turkey
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Published: 1 August 2005
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Abstract

In plane Lorentzian geometry it is studied points, timelike, spacelike and lightlike lines, triangles, etc [4]. On the hyperbolic sphere, there are points, but there are no straight lines, at least not in the usual sense. However, straight timelike lines in the Lorentzian plane are characterized by the fact that they are the shortest paths between points. The curves on the hyperbolic sphere with the same property are hyperbolic circles. Thus it is natural to use these circles as replacements for timelike lines. The formulas for the sine and cosine rules are given for the Euclidean sphere 2 S [2, 3, 6] and hyperbolic sphere [5]. In this study, we obtained formulas related with the spacelike angles and hyperbolic angles corresponding to the sides of geodesic triangles on hyperbolic unit sphere \(H_{0}^{2}\).
Keywords: Geodesic triangle; Lorentzian space; Timelike vector Geodesic triangle; Lorentzian space; Timelike vector
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Özdemir, A.; Kazaz, M. Hyperbolic Sine and Cosine Rules for Geodesic Triangles on the Hyperbolic Unit Sphere \(H_{0}^{2}\). Math. Comput. Appl. 2005, 10, 203-209.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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