id: 27983
Title: The investigation of conditions of the extreme arrangement of several classical geometric figures with a common center by estimating the length of the line and the area of their divergence
Authors: Dubchak V., Manzhos E.
Keywords: circle, square, equilateral triangle, length of the arc of a circle and its part, length of the side of the square, area, extremality of functions of one variable
Date of publication: 20210303 15:00:40
Last changes: 20210303 15:00:40
Year of publication: 2021
Summary: The article deals with the question of the optimal, extreme (minimum) location of one flat figure, namely, a square in the first case, as well as an equilateral triangle in the second case relative to a circle with a common center of these figures. The main criterion for the optimality of such mutual placement of one figure relative to another are such criteria as the effective location of the total length of the set of lines, according to which the discrepancy of these figures and the estimate of the area of their discrepancy occur. The value of a certain function that determines the length of the sum of the lines of discrepancy of the figures in both cases and the function that determines the area of discrepancy is obtained. A study of the extremality of such functions has been performed and it has been shown that at the found point of the extremum, the function determines the total length of the line of divergence of the figures and the corresponding area of divergence acquires extreme values. Figures are given for a better understanding of the formulation and solution of the problem. Conclusions are made in which the values of the required arguments are given and the corresponding function will acquire extreme values.
URI: http://repository.vsau.org/repository/getfile.php/27983.pdf
Publication type: Статті у зарубіжних наукових фахових виданнях (Copernicus та інші)
Publication: Slovak international scientific journal. 2021. № 49., vol. 1. Р. 2129.
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