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Calculation of the tortuosity of the boundaries of flat figures

Abstract

Calculation of the tortuosity of the boundaries of flat figures

Egereva E. N., Chopurov K.A.

Incoming article date: 24.05.2019

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