Geometric transformations and maple applications

This thesis consists of five chapters. In the introduction chapter; we give some information about the historical developments of our study. In the material and method chapter, vector space, Affine space, Euclidean space, Euclidean frame, Euclidean coordinate system, line and plane equations, states of two lines with respect to each other, states of two planes relative to each other, states of line and plane with respect to each other, fundamentals about line and plane concepts are given. In addition, concepts related to vectors, matrix and matrix operations, Fibonacci and Lucas numbers, Fibonacci and Lucas vectors and its properties are given. In the main results section, the matrix combinations of the transformations in two-dimensional and three-dimensional space are expressed. The transformations in Euclidean 3-space of Fibonacci and Lucas 3-vectors have been studied. Some properties of the Fibonacci and Lucas numbers, Fibonacci and Lucas vectors are given. After defining the Householder transformation and the -dimensional Fibonacci and Lucas vectors, the Householder transformation is given for the more specific Fibonacci and Lucas 3-vectors. Also, the applications and codes of the transformations in Maple program were created. In the fourth chapter, after the conclusions and suggestions of our study were given, the bibliography was written in the last chapter.