Cayley formula, Euler parameters for homothetic motions and their applications

This study consists of six sections. In the first section, literature review and the aim of the study are given. In the second section, basic concepts firstly for E^n, n-dimensional, E^3, 3-dimensional Euclidean spaces and then for E^1_n, n-dimensional and E^1_3, 3-dimensional Lorentzian spaces are given. Besides some definitions and theorems which belongs to these spaces are presented for general and homothetic motions. In the third section, some studies and indications about Cayley formula, Euler – Rodrigues parameters and rotation axes of motions are given for general motions in Euclidean and Lorentzian spaces. The fourth section and the rest of this study constitute original parts of the thesis. In this section, Cayley formula is obtained in E^n, n-dimensional Euclidean space and Cayley transformation, Euler – Rodrigues parameters, rotation axises of motions are obtained in E^3, 3-dimensional Euclidean space for homothetic motions. In the fifth section, indications which are obtained in fourth section are given for Lorentzian space. Additionally, distinctions which occurs from the differences of notions of spacelike and timelike are detailed reviewed. Then the definitions and the theorems are presented comparatively. In the sixth and last section, the conclusions which are obtained in this study and suggestions for the next studies are given.