Loxodromes on helicoidal surfaces and tubes withvariable radius in euclidean 4-space

In the first part of this thesis, the studies regarding loxodromes in Euclidean 3-space were mentioned. Also, rotational surfaces, helicoidal surfaces and tubes with variable radius surfaces in Euclidean 4-space were mentioned. In the second part, some fundamental definitions and formulas related to curves and surfaces in were given. In the third chapter, definitions and parameterizations of the rotational surfaces and helicoidal surfaces in Euclidean 3-space are given. Then, the equations of loxodromes were obtained and some examples were given. In the fourth section, the definition and parameterization of the canal surface in Euclidean 3-space is given. Then the equations of loxodromes were obtained and some examples were given. In the fifth chapter, the parametrizations of loxodromes on helicoidal surfaces and rotational surfaces in were found. In addition, an example is given and relevant graphs are drawn. In chapter six, the parametrizations of loxodromes on tubes with variable radius in were found. An example is also given and relevant graphs are drawn.