🚀 go-pugleaf

In article <slrn5jd935.b8j.sitaram@mohin.cse.iitb.ernet.in>, Sitaram
Iyer <sitaram@mohin.cse.iitb.ernet.in> writes
>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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When I tried this iteration 1/b[i] did not converge on pi at all.
Perhaps I misunderstood.  Can anyone make the statement of the iteration
clearer?
-- 

Martin Ward

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"When *I* use a word", Humpty Dumpty said in rather a scornful tone, "it
 means just what I choose it to mean - neither more nor less".
"The question is", said Alice, "whether you *can* make words mean so many
 different things".
"The question is", said Humpty-Dumpty, "which is to be master - that's all".

"Through the Looking-Glass" - Lewis Carroll.
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