A characterization of conchoid curves and surfaces in euclidean spaces

In this thesis, conchoid curves and surfaces in Euclidean space are considered. This thesis consists of four chapters. The first chapter is the introduction. The second chapter contains some well-known definitions and terms about curves and surfaces in Euclidean space which will be used in other chapters. In the third chapter, conchoid curves are defined on plane and 3- dimensional Euclidean space. Furthermore, the curvatures of these curves are calculated and the results are given. According to the results, some examples are given and plot their graphics. In the fourth chapter, conchoidal surfaces are studied in 3 and 4- dimensional Euclidean space. Firstly, in the 3- dimensional Euclidean space, the results of the curvature of the conchoidal surface are obtained. Also, the results are given of the surface of revolution obtained by rotating a planar conchoid curve in 3- dimensional space and are plotted the graphics of the surface. Finally, the definition of the conchoidal surface in the 4- dimensional Euclidean space is given. Also some results are obtained that these surfaces become flat and minimal. In the last part the rotational surfaces in the 4- dimensional space and the meridian surfaces are conchoidal surfaces are given as examples.