Solving Pi

[Tim Kelley]

In article <11307 at watnot.UUCP> cagordon at watnot.UUCP (Chris A. Gordon) writes:
>In article <187 at ski.UUCP> eeg at ski.UUCP (eeg systems (bcx) writes:
>[ article deleted - program to calculate pi to X digits ]
>>**	      infinity                    infinity
>>**	      ____  16*(-1e(k+1))         ____  4*(-1e(k+1))
>>**	      \                           \
>>**	pi =   >    -------------    -     >    ------------     (Expression 1)
>>**	      /                           /
>>**	      ----  (2k-1)*5e(2k-1)       ----  (2k-1)*239e(2k-1)
>>**	      k = 1                       k = 1
>>**
>
>Here is a more simple sum-evaluation of pi (thought I don't know if it will work
>with the original program):
>
>               oo
>              ----         k-1
>         |  | \        (-1)
>    pi = +--+  >    ----------                 (Expression 2)
>	    | /       2k-1
>	      ----
>	      k=1

Friends, I hate to include the complete text of the article I'm responding
to but I have no alternative. The reason expression 1 is better than 
expression 2 is that the series in 1 converges faster than that in 2.
One can check this out with a programmable calculator. Expression 2 will
run all night and give you maybe 3 figures.  If you want 3 digits of accuracy
from expression 2 you'd need about 1000 terms; 4 digits would require 10,000.

-- 
C.T. Kelley  decvax!mcnc!ecsvax!ctk
Dept. of Math.    N.C. State U. Box 8205
Raleigh, N.C. 27695-8205,  919-737-7895