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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2005, 10(2), 203-209;

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
Author to whom correspondence should be addressed.
Published: 1 August 2005
PDF [224 KB, uploaded 31 March 2016]


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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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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