Approximations of the Number π Using Onscribed Regular Polygons

Szyszkowicz, Mieczysław (2016) Approximations of the Number π Using Onscribed Regular Polygons. British Journal of Mathematics & Computer Science, 14 (5). pp. 1-7. ISSN 22310851

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Abstract

Circa 255 B.C., Archimedes invented a method for approximating the value of the number π. He used the perimeters of the inscribed and circumscribed regular polygons to approximate the perimeter of a circle. Starting with two regular hexagons, he doubled the number of their sides up to 96. This approach allowed him to obtain lower and upper estimations of π. He showed that its value lies in the interval [3 + 10/71, 3 + 1/7]. Here the use of onscribed regular polygons is proposed for a similar purpose. The onscribed regular polygons are placed between the two polygons used in Archimedes’ method. Their location is unique and well defined by applying a criterion to minimize distances. The sequences of areas and perimeters produced by these regular polygons, and their linear combinations, generate values which better approximate π than many other geometrical methods.

Item Type: Article
Subjects: Middle East Library > Mathematical Science
Depositing User: Unnamed user with email support@middle-eastlibrary.com
Date Deposited: 14 Jul 2023 11:42
Last Modified: 21 Sep 2024 04:26
URI: http://editor.openaccessbook.com/id/eprint/955

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