Re: Re: how to compute pi by using continued fraction?
- To: mathgroup@smc.vnet.net
- Subject: [mg12034] Re: [mg11979] Re: how to compute pi by using continued fraction?
- From: wself@viking.emcmt.edu (Will Self)
- Date: Fri, 24 Apr 1998 01:52:06 -0400
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