Euclidean, complex and lorentzian geometry of the fibonacci vectors

This study has been subject to Fibonacci vectors, generalized Fibonacci vectors and properties of them. Also, inner product, vector product and triple scalar product for Fibonacci vectors are given. This thesis consists of six chapters. In the first chapter the aim of the thesis and the review of the literature are given. The basic concepts are described in the second chapter. The third chapter of the thesis is one of the original part. In the third chapter the corresponding anti-symmetric matrix for Fibonacci 3-vectors are examined. The vector product by using this anti-symmetric matrix is reconsidered. The vector product for Fibonacci 4-vectors and Fibonacci 7-vectors are described. Furthermore, the corresponding anti-symmetric matrix for Fibonacci 7-vectors and properties of vector product by using this anti-symmetric matrix are given. Moreover, in the fourth chapter, complex Fibonacci 3-vectors are investigated, vector product of two complex Fibonacci vectors is defined and properties of vector product are given. Furthermore, in the fifth chapter Fibonacci 3-vectors, Fibonacci 4-vectors and Fibonacci 7-vectors are examined at Lorentz-Minkowski space. In the sixth chapter overview of the study is given.