Programming Pi

 BBS: Inland Empire Archive
Date: 05-07-92 (20:44)             Number: 130
From: ROB FLOR                     Refer#: NONE
  To: ANDY KIDLE                    Recvd: NO  
Subj: Programming Pi                 Conf: (2) Quik_Bas
AK>I need some help with a simple computer program (or what should be
  >simple for a semi-experienced programmer.)  I need to program two
  >infinite mathematical series for finding pi.  I have access to BASIC and
  >QUICKC for programming.  Here are the two series,
  >so if you can help, let me know:

AK>pi = 4(1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 +......)

  The way I would approach this is to approach the limit of precision
  for the divisor, and then do the final division:
DefDbl A-Z

Y = .000000000000050        'pick a cutoff near machine limits
Si = - 1

 FOR K = 3 TO 65535 STEP 2         ,K = 3.00000..., 5.00000..., 7.00..,etc
    X =  Si * 1 \ k                '-1/3, +1/5, -1/7 etc
    If ABS(X) < Y THEN EXIT FOR    'Machine's limit of computabilty
    Divisor = Divisor + X          'add X
    Si = Si * -1                   'flip sign for next computation

Pi = 4 \ Divisor

   This is untested, so lets call it pseudocode.  The alogorithm seems
sound, but not a lot of thought went into it.

 AK>I'll have to write out the second one since their are no keys to
>represent exponents and square roots:

       Exponent = ^ as in 2^3,  square root = X^.5


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