🚀 go-pugleaf

On 19 Mar 97 09:50:35 GMT, Belinda Berry wrote:
: 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.
: -- 
: Belinda Berry
: <BJBerry@onaustralia.com.au>

There was this very fast converging iteration:
Start with a(0) = sqrt(2)-1 and b(0) = 6 - 4*sqrt(2)

t =  (1-a[i-1]^4)^(0.25)
a[i] = (1-t)/(1+t)
b[i] = (1+a[i])^4 * b[i-1] - 2^(2*i+1) * a[i] * (1+a[i]+a[i]^2)

1/b[i] is supposed to converge to PI VERY fast, within 3 iterations it
fills up double precision and within a (don't remember) dozen or so
iterations it gives millions of digits. Can someone elaborate ?

- Sitaram.
--
Thanx.
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| Sitaram Iyer <sitaram@[144.16.111.2]>  http://www.cse.iitb.ernet.in/~sitaram |
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