Apollonius curves on the sphere surface

This study which is related to the Apollonius curves on the unit sphere surface S^2 consists of three chapters.In the first chapter, basic concepts of vectors are mentioned. Also in this chapter, some definitions and theorems of curves which are essential for our study are mentioned.In the second chapter, Apollonius curves and surfaces are defined in the Euclidean plane R^2, Euclidean space R^3, and the plane z=sy of Euclidean space R^3, and the related theorems are given and proved. Furthermore, the examples of Apollonius curves and surfaces are given in these spaces.In the third chapter, as similar of Apollonius curves which are defined in the Euclidean plane and the Euclidean space, spherical Apollonius curves on the unit sphere surface S^2 are defined and the related theorems are given and proved. Furthermore, the examples of Apollonius curves are given on this surface. The results obtained are also valid on any surface of a sphere.