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  1. Newsgroups: rec.puzzles
  2. Path: sparky!uunet!utcsri!geac!zooid!r-node!amichail
  3. From: amichail@r-node.gts.org (Ashraf Michail)
  4. Subject: Re: Formulae for pi
  5. Message-ID: <1992Nov15.193400.8408@r-node.gts.org>
  6. Organization: R-node Public Access UNIX Information System (416-249-5366)
  7. References: <1992Nov6.163504.17171@husc15.harvard.edu>
  8. Date: Sun, 15 Nov 1992 19:34:00 GMT
  9. Lines: 17
  10.  
  11. This is the best algorithm I know for generating PI:
  12.  
  13. y0=SQRT(2) -1                       
  14. a0=6-4*SQRT(2)
  15.  
  16. y1=(1-(1-y0^4)^(1/4))/(1+(1-y0^4)^(1/4))
  17. a1=((1+y1)^4)*a0-(2^3)(y1(1+y1+(y1)^2)
  18.  
  19. y2=(1-(1-y1^4)^(1/4))/(1+(1-y1^4)^(1/4))
  20. a2=((1+y2)^4)*a1-(2^5)(y2(1+y2+(y2)^2)
  21.  
  22. and so on ...
  23.  
  24. 1/(a15) will give more than two billion digits of PI..
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