How to get many places of pi from Machin's Equation?
Richard D. Moores
rdmoores at gmail.com
Sat Jan 9 12:31:49 CET 2010
Machin's Equation is
4 arctan (1/5) - arctan(1/239) = pi/4
Using Python 3.1 and the math module:
>>> from math import atan, pi
>>> pi
3.141592653589793
>>> (4*atan(.2) - atan(1/239))*4
3.1415926535897936
>>> (4*atan(.2) - atan(1/239))*4 == pi
False
>>> abs((4*atan(.2) - atan(1/239))*4) - pi < .000000000000000001
False
>>> abs((4*atan(.2) - atan(1/239))*4) - pi < .0000000000000001
False
>>> abs((4*atan(.2) - atan(1/239))*4) - pi < .000000000000001
True
>>>
Is there a way in Python 3.1 to calculate pi to greater accuracy using
Machin's Equation? Even to an arbitrary number of places?
Thanks,
Dick Moores
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