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  1. Newsgroups: sci.math
  2. Path: sparky!uunet!mcsun!news.funet.fi!news.cc.tut.fi!jk87377
  3. From: jk87377@cc.tut.fi (Juhana Kouhia)
  4. Subject: Re: Pi in beatiful form --lost
  5. Message-ID: <1992Dec19.040954.6498@cc.tut.fi>
  6. Organization: Tampere University of Technology
  7. References: <BzBt9q.2HM@unccsun.uncc.edu> <1gmvieINN7al@aludra.usc.edu> <1992Dec16.201741.24270@CSD-NewsHost.Stanford.EDU>
  8. Date: Sat, 19 Dec 92 04:09:54 GMT
  9. Lines: 16
  10.  
  11.  
  12. In article <1992Dec16.201741.24270@CSD-NewsHost.Stanford.EDU>
  13. pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
  14. >
  15. >And then there is the oldest formula, Vieta's product from 1593:
  16. >
  17. >2/pi = sqrt(1/2) * sqrt((1+sqrt(1/2))/2) * ...
  18.  
  19.  
  20. Hmm...
  21.  
  22.  pi = lim_{n \to \infty} 2^{n+1} sqrt(2 - sqrt(2+sqrt(2+sqrt(2+...))))
  23.                                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^
  24.                                                      n items
  25.  
  26.  
  27. Juhana Kouhia
  28.