On gyrohyperbolas

This thesis consists of five chapters. In the first chapter, information and literature researches about the subject studied and the aim of the thesis are given. In the second chapter, gyrogroups and gyrovector spaces are introduced and some basic concepts and propositions used in gyroalgebra are given. In the third chapter, the definitions of barycentric coordinates which have an impor-tant place in the study of gyrohyperbolas are given and the construction of some hyperbolic structures such as gyroangles and gyrotriangles are examined. In the fourth chapter, some results of hyperbolas in Euclidean plane were obtained by using definition and some properties of gyrohyperbollas in Einstein gyrovector spaces. In the fifth and last chapter, the contributions to the literature and the results are given in the light of the obtainments.