Random Polygons and Estimations of π

In this paper, we study the approximation of through the semiperimeter or area of a -sided polygon inscribed in a unit circle in ℝ . We show that, with probability 1, the approximation error goes to 0 as → ∞, and is roughly sextupled when compared with the classical Archimedean approach of using a r...

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 17; no. 1; pp. 575 - 581
Main Authors Xu, Wen-Qing, Meng, Linlin, Li, Yong
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 22.06.2019
De Gruyter Poland
Subjects
65C50
Approximation
Archimedean polygon
Borel-Cantelli lemma
extrapolation
Mathematical analysis
Polygons
Primary 00A05
random division
random polygon
Secondary 60D05
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Summary:In this paper, we study the approximation of through the semiperimeter or area of a -sided polygon inscribed in a unit circle in ℝ . We show that, with probability 1, the approximation error goes to 0 as → ∞, and is roughly sextupled when compared with the classical Archimedean approach of using a regular -sided polygon. By combining both the semiperimeter and area of these random inscribed polygons, we also construct extrapolation improvements that can significantly speed up the convergence of these approximations.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2019-0049