Date: Jan 13, 2012 11:19 AM
Author: Joe Niederberger
Subject: Re: Brainstorming about STEM (was About Functions)

Just an interesting tidbit about pi...

Kirby mentions:
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Look carefully at this expression for 1/pi by Ramanujan.

There is no symbolic chain of reasoning going on for many pages to
back it up, neither in the form of a derivation nor a proof.

http://worldgame.blogspot.com/2008/02/reflective-fragment.html
(graphic, middle of the column)
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Unfortunately the link seems broken now. I was reminded of this when I came across this interesting formula that allows one to calculate digits of pi essentially starting at any place -- a remarkable formula whcich seems to have been around for over ten years now...

See: http://www.ams.org/samplings/feature-column/fcarc-pi

Interestingly, this formula was discovered by a sort of combination of human and computer algorithm (the PSLQ algorithm) as described in the article. (if the humans involved in the effort were not dreaming of Hindu goddesses, perhaps the alogorithm was.)

The resultant formula has been useful in looking at the question of whether the digits of pi are "random" in a certain sense:
http://www.eurekalert.org/features/doe/2001-07/dbnl-atd062002.php

Joe N