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Kyungpook Mathematical Journal 2020; 60(2): 375-385

Published online June 30, 2020

Copyright © Kyungpook Mathematical Journal.

On Interpretation of Hyperbolic Angle

Buşra Aktaş, Halit Gündoğan, Olgun Durmaz*

Department of Mathematics, Faculty of Science and Arts University of Kirikkale, 71450-Yahşihan, Kirikkale, Turkey
e-mail : baktas6638@gmail.com and hagundogan@hotmail.com
Department of Mathematics, Faculty of Science University of Atatüurk, 25240-Yakutiye, Erzurum, Turkey
e-mail : olgun.durmaz@atauni.edu.tr

Received: October 5, 2018; Revised: February 3, 2019; Accepted: March 4, 2019

Abstract

Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

Keywords: special relativity, hyperbolic angle, Bondi factor