🚀 go-pugleaf

In article <01bc3440$d8a87040$LocalHost@default>, Belinda Berry
<BJBerry@onaustralia.com.au> writes
>How do you actually calculate pi anyway. (without loooking it up in a
>book.) I suppose if you drew up a really accurate circle and did some
>measuring it might work, but nothing I draw could possibly get more than
>about 2 decimal places.

Quite right, Belinda, not even the most accurate drawing and measuring
could produce results good for many more places than that.

Series are the traditional way of calculating numbers like pi to lots of
places.  For example:

(pi^2)/6 = 1+(1/2^2)+(1/3^2)+(1/4^2)+...

The series goes on for ever, but the terms get smaller and smaller and
the sum is said to "converge", in this case "converge to pi squared over
six". For a given degree of accuracy we can stop after a while.  This
particular series is easy to state but converges very slowly, so "after
a while" means after a *long* while.  For example, to get four decimal
places of accuracy we have to add up 6918 terms.  Fortunately there are
other series which converge more rapidly.
-- 

Best wishes

Martin Ward

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"No-one is ever hurt by the truth - he is injured who continues in
 self-deception and ignorance."          Marcus Aurelius
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