On Sat, Jan 9, 2010 at 07:57, Mark Dickinson <dicki...@gmail.com> wrote: > On Jan 9, 11:31 am, "Richard D. Moores" <rdmoo...@gmail.com> wrote: >> Machin's Equation is >> >> 4 arctan (1/5) - arctan(1/239) = pi/4 >> [...] >> >> 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? > > Here's some crude code (no error bounds, possibility of infinite > loops, ...) that computes pi to 1000 places using Machin's formula and > the decimal module. The last few digits will be bogus, and should be > ignored. > > from decimal import Decimal, getcontext > > def atan(x): > # reductions > reductions = 0 > while 100*abs(x) > 1: > reductions += 1 > x /= 1 + (1+x*x).sqrt() > > # Taylor series > sum = 0 > xpow = x > x2 = x*x > k = 1 > while True: > term = xpow/k > oldsum = sum > sum += term > if sum == oldsum: > break > k += 2 > xpow *= -x2 > > return sum * 2**reductions > > getcontext().prec = 1000 > one = Decimal(1) > print(16*atan(one/5) - 4*atan(one/239)) > -- > http://mail.python.org/mailman/listinfo/python-list >
Great! Done in Python 3 with arctan and the decimal module. And the first 997 digits were accurate. Just what I was after. I don't believe the Chudnovsky algorithm has been mentioned. It isn't what I wanted, but it is amazing. (<http://pastebin.com/f2a77629f>) Thanks, everyone! Dick Moores -- http://mail.python.org/mailman/listinfo/python-list
