Types of Fibonacci numbers and their usage in quaternions

This thesis consists of three chapters. First chapter provides the aim and the scope of the study. The second chapter gives the basic definitions and terms related to the subject of the thesis. In the third chapter, description of dual Fibonacci numbers, theorems for basic identities, D'Ocagnes, Catalan and Cassini identities, theorems expressing negadual Fibonacci and negadual Lucas numbers and Binet formulas of dual Fibonacci numbers are given. Also, description of dual Fibonacci vectors, the dot product and cross product of two dual vectors and the mixed product of three dual vectors are presented. Finally, we provide the descriptions of dual Fibonacci quaternion and dual Lucas quaternion, the addition and multiplication operations on the dual Fibonacci quaternion and theorems including basic identities.