The paper considers the tortuosity of regular n-gons, fractals and the tortuosity of the boundaries of a rectangular trapezium. The tortuosity value ωn is obtained in the limiting case. For all the considered figures, the dependencies of the tortuosity values on the number of sides of the regular n-gon and on the nth iteration for the fractal in question were constructed. For the boundary of a rectangular trapezoid, we plotted the curves of the tortuosity border on the angular coefficient of the straight line y = px + q, which bounds the trapezoid under consideration. It is shown that with an increase in the number of iterations in each fractal, the value of tortuosity increases, and its limiting value tends to infinity.

Keywords: Tortuosity, closed loop, fractal, regular n-squares, Koch's snowflake, contour boundaries

The paper deals with the derivation of the basic relations of the theory of finite rotations. A numerical study of the dependence of the guide cosine of the final rotation on the guide cosines of a fixed coordinate system and the coordinate system associated with a solid is carried out. The formulas for the cosines of the angle of final rotation are obtained. The developed program of calculation of the values of the guides of the cosines of the final turning of the quantities in the problem statement. A graph of the dependence of the guide cosine of the final turn on the sine of the angle of the final turn. This dependence is clearly displayed when the program is started.

Keywords: vector orientation in space, spherical trigonometry, finite rotation angle, guiding cosine, Euler angles, finite rotation