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Article

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

by
A. Özdemir
and
M. Kazaz
*
Department of Mathematics, Celal Bayar University, Muradiye Campus, 45047, Manisa, Turkey
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2005, 10(2), 203-209; https://doi.org/10.3390/mca10020203
Published: 1 August 2005
Versions Notes

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

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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. https://doi.org/10.3390/mca10020203

AMA Style

Özdemir A, Kazaz M. Hyperbolic Sine and Cosine Rules for Geodesic Triangles on the Hyperbolic Unit Sphere \(H_{0}^{2}\). Mathematical and Computational Applications. 2005; 10(2):203-209. https://doi.org/10.3390/mca10020203

Chicago/Turabian Style

Özdemir, A., and M. Kazaz. 2005. "Hyperbolic Sine and Cosine Rules for Geodesic Triangles on the Hyperbolic Unit Sphere \(H_{0}^{2}\)" Mathematical and Computational Applications 10, no. 2: 203-209. https://doi.org/10.3390/mca10020203

APA Style

Özdemir, A., & Kazaz, M. (2005). Hyperbolic Sine and Cosine Rules for Geodesic Triangles on the Hyperbolic Unit Sphere \(H_{0}^{2}\). Mathematical and Computational Applications, 10(2), 203-209. https://doi.org/10.3390/mca10020203

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