Approximations of the Number π Using Onscribed Regular Polygons
Journal of Advances in Mathematics and Computer Science · pp. 1–7 · Published 11 Feb 2016
10.9734/BJMCS/2016/23947Abstract
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.
Cited by 1
Mieczyslaw Szyszkowicz · The Mathematical Gazette · 2019
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