Affine transformation on real, complex and hyperbolic plane and i̇ts aplications

This thesis consists of three parts. In this thesis, affine transformations and applications in real, complex and hyperbolic plane are discoursed. In the first chapter, five axioms of Euclide and three axioms of affine transformation and the definition of affine transformation are given. In the second chapter, the basic properties of affine transformations and the fundamental theorem of affine theorem are proved in the real plane. In addition, an affine conversion of the cones in the real plane into the center-like cone has been demonstrated. Affine transformations in the complex plane are indicated by f(z) = Az + Bz + C, where A;B;C is complex number: The relation of the type of f afin transformation with A, B, C coefficients was investigated. Fractal samples are given as an application of affine transformations in the complex plane. In the third chapter, the affine transformations in the hyperbolic plane are shown with a transformation of f(z) = Az+Bz+C where A;B;C is hyperbolic number. The relation of the type of f afin transformation with A, B, C coefficients was investigated. Fractal samples are given as an application of affine transformations in the hyperbolic plane.