Flat area characteristics of polygons circumscribing parabolic figures

Elvira Egereva,Zakhar Nepovinnyy,Dmitry Surovtsev,A Zheltenkov,A Mottaeva

doi:10.1051/e3sconf/202016402004

Elvira Egereva, Zakhar Nepovinnyy + Show 3 more

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https://doi.org/10.1051/e3sconf/202016402004

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Abstract

The works elucidates the extremum areas of the polygons circumscribing parabolic figures. It is shown that the ratio of the areas of the polygons circumscribed near parabolic figures to the areas of the corresponding figures always remains a constant value, independent of the coefficients characterizing the quadratic function. The only point at which the function under study reaches its minimum value is found. The question of the necessary conditions for the existence of a circle circumscribed about a parabolic quadrilateral found in the Ptolemy theorem is being considered.

Highlights

The article explores the relationship between the values of the areas of parabolic figures and the minimum values of the areas of polygons described near parabolic figures
Among the results obtained by Lao and Mayer, considered in [3], limit theorems for the maximum perimeter and maximum area of random triangles inscribed in a circle are of great interest
If for a parabolic quadrilateral S1 and S2 are the areas of triangles F1 and F2 соответственно, respectively, the dimensionless parameter is calculated by the formula δ

Summary

Introduction

The article explores the relationship between the values of the areas of parabolic figures and the minimum values of the areas of polygons described near parabolic figures. The study of the area of figures of various configurations has always attracted the attention of scientists [1]. This knowledge is applied in many branches of science and technology. The authors of [2] found an algorithm for finding a convex polygon with a maximum area described near a given polygon. Among the results obtained by Lao and Mayer, considered in [3], limit theorems for the maximum perimeter and maximum area of random triangles inscribed in a circle are of great interest. In [3], the problem for the minimum perimeter and the minimum area bounding m - polygons (m≥3), which has not yet been studied, is considered

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