General Mathematics

    

Approximation of pi

Authors: Mieczyslaw Szyszkowicz

Archimedes used the perimeter of inscribed and circumscribed regular polygons to obtain lower and upper bounds of the number pi. He started with two regular hexagons and he doubled their sides from 6 to 12, 24, 48, until 96. Applying the perimeters of 96 side regular polygons, Archimedes obtained the bounds for the number pi: 3+10/71<pi<3+1/7. His algorithm can be executed as a recurrence formula called the Borchardt-Pfaff-Schwab method. Dörrie proposed an improvement of this algorithm to produce narrower interval which encapsulates pi. Here a linear combination of the bounds is realized to obtain an improved accuracy. Many other linear combinations are presented to approximate this mathematical constant.

Comments: 5 Pages.

Download: PDF

Submission history

[v1] 2026-02-15 10:06:26

Unique-IP document downloads: 133 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus