home *** CD-ROM | disk | FTP | other *** search
/ NetNews Usenet Archive 1992 #27 / NN_1992_27.iso / spool / rec / puzzles / 7293 < prev    next >
Encoding:
Text File  |  1992-11-15  |  1.1 KB  |  36 lines
  1. Newsgroups: rec.puzzles
  2. Path: sparky!uunet!wupost!darwin.sura.net!convex!news.utdallas.edu!corpgate!crchh327!crchh410!bcash
  3. From: bcash@crchh410.BNR.CA (Brian Cash)
  4. Subject: Re: Formulae for pi
  5. Message-ID: <1992Nov16.052144.23407@bnr.ca>
  6. Sender: news@bnr.ca (News on crchh327)
  7. Nntp-Posting-Host: crchh410
  8. Reply-To: bcash@crchh410.BNR.CA (Brian Cash)
  9. Organization: Bell-Northern Research Ltd.
  10. References: <1992Nov6.163504.17171@husc15.harvard.edu> <1992Nov15.193400.8408@r-node.gts.org>
  11. Date: Mon, 16 Nov 1992 05:21:44 GMT
  12. Lines: 22
  13.  
  14. In article <1992Nov15.193400.8408@r-node.gts.org>,
  15. amichail@r-node.gts.org (Ashraf Michail) writes:
  16. |>This is the best algorithm I know for generating PI:
  17. |> 
  18. |>y0=SQRT(2) -1                       
  19. |>a0=6-4*SQRT(2)
  20. |> 
  21. |>y1=(1-(1-y0^4)^(1/4))/(1+(1-y0^4)^(1/4))
  22. |>a1=((1+y1)^4)*a0-(2^3)(y1(1+y1+(y1)^2)
  23. |> 
  24. |>y2=(1-(1-y1^4)^(1/4))/(1+(1-y1^4)^(1/4))
  25. |>a2=((1+y2)^4)*a1-(2^5)(y2(1+y2+(y2)^2)
  26. |> 
  27. |>and so on ...
  28. |> 
  29. |>1/(a15) will give more than two billion digits of PI..
  30. |> 
  31.                
  32. Don't your roots need to be taken to two billion digits, then?
  33. (to prevent rounding errors)
  34.  
  35. Brian /-|-\
  36.