The concept of angle in real and dual spaces

This Thesis consists of four chapters.In the first chapter Affine Frame, Distance, Euclidean Frame, Euclidean Angles are presented.In the second chapter Spacelike, Timelike, Lightlike Planes in Minkowski 3-Space,The Concept of Angle related this planes and examples are given.In the third chapter basic concepts of Dual Geometry is given. E. Study mapping is stated and proved in this geomety and fundamental examples are presented.In the fourth chapter Dual Lorentzien Space and fundamental concepts of this space are defined. E. Study mappings for oriented timelike, spacelike and lighlike line of Real Lorentzien Spaces are stated and proved. Geometric interpretation of this mappings is illustrated with figures and elemanter examples are given. As an addition to E. Study mappings, Lorentzien geometric interpretation of Dual Lorentzien Angles presented with fundamental examples.