Projection areas of the surfaces obtained kinematically

This thesis consists of seven chapters. In the first chapter, review of the literature and the aim of the thesis are given. In the second chapter, some basic concepts of the curves and surfaces are described. In the third chapter, by taking the parameter curves of a regular surface with non-umbilical and flat points as curvature lines, the derivative equations of the frame composed of the unit velocity vectors of the parameter curves and the unit normal vector of the surface are expressed with the help of the principal curvatures and geodesic curvatures of the parameter curves. The fourth, fifth and sixth chapter are the original chapters of this thesis.In the fourth chapter, under special two-parameter motion, the area of the projection area of the orbit surface of a point is calculated. Also, the relation between the projection areas of the orbit surfaces of the end points of a fixed length straight line segment and the projection area of the other orbit surface taken on the straight line segment are investigated. Then the relation between the projection areas of the orbit surface of non-collinear points and the relation between the projection areas of the other orbit surfaces taken within the triangle indicated by these three points are investigated. In the fifth chapter, under special two-parameter homothetic motion, the projection area of orbit surface of a point on a plane is calculated. In the sixth chapter, applications are given. In the last chapter, conclusion and suggestions are given.