Programming Pi

 BBS: Inland Empire Archive
Date: 05-08-92 (19:28)             Number: 190
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 +......)


I made a suggestion to calculate each irrational number but that would
give poor accuracy since irrational numbers cannot be calculated
precisely.


Lets see if we can avoid this by finding the old fashion Common
Denominator:


 A/B - C/D = (A*D / B*D) - (C*B / D*B) =

 1/1 - 1/3 = (1*3 / 1*3) - (1*1 / 3*1) =

 3/3 - 1/3 = (3-1) / 3 =    2/3

A now = 2      'no imprecision
B now = 3      'no division, no floating point

'=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
DEFINT A - Z

A=1 :B=1 :C=1 :Sign=0
N = 15  'lets say

FOR D = 3 TO N STEP 2
   Sign = NOT Sign

  'Find common denominator, A*D/B*D, C*B/D*B

   C = B * Sign  'c is always + or - 1

   B = B * D     'D*B = B*D so we already have common denominator


   A = A * D     'multiply top and bottom by same amount


   A = A + C     'calculate dividend, A + [+|-]C

   PRINT "Intermediate calculation of pi = 4 divided by ( "A"/"B" )"
NEXT K


  pi# = 4# / (A / B)   'our only division

  print "pi to "N" calculations ="pi#


'  Rob


 * OLX 2.2 * pi of the day


--- WM v2.01/91-0156
 * Origin: BEAR HEAVEN BBS (914) 677-6948 MILLBROOK NY (1:272/53)