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MathGroup Archive 1998

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Re: Re: how to compute pi by using continued fraction?



Craig P Earls wrote:

>>>>>>>>

Here is a continued fraction definition of Pi attributed to Ramanujan
that definitely has a pattern:

Pi              1
-- =     --------------
4          1 +    1
               ---------
                    3^2          <---The pattern is odd numbers
               2+ --------
                      5^2
                  2+ -------
                        ...

<<<<<<<<

In fact, that continued fraction expansion is due to Lord Brouncker
(1620-1684) who produced it from John Wallis' (1616-1703) original
infinite product

4/Pi = 3/2 * 3/4 * 5/4 * 5/6 * 7/6 * 7/8 * 9/8 ...


Will Self



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