On Dec 11, 8:16 am, Anh Hai Trinh <anh.hai.tr...@gmail.com> wrote: > I'm just curious which formula for pi is given here: <http:// > docs.python.org/library/decimal.html#recipes>? > > def pi(): > """Compute Pi to the current precision. > > >>> print pi() > 3.141592653589793238462643383 > > """ > getcontext().prec += 2 # extra digits for intermediate steps > three = Decimal(3) # substitute "three=3.0" for regular > floats > lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24 > while s != lasts: > lasts = s > n, na = n+na, na+8 > d, da = d+da, da+32 > t = (t * n) / d > s += t > getcontext().prec -= 2 > return +s # unary plus applies the new precision > > It looks like an infinite series with term `t`, where`n` = (2k-1)^2 > and `d` = d = 4k(4k+2) for k = 1... Does it have a name?
Interesting. So the general term here is 3 * (2k choose k) / (16**k * (2*k+1)), k >= 0. Python 3.2a0 (py3k:76334:76335, Nov 18 2009, 11:34:44) [GCC 4.0.1 (Apple Inc. build 5490)] on darwin Type "help", "copyright", "credits" or "license" for more information. >>> from math import factorial as f >>> 3*sum(f(2*k)/f(k)/f(k)/(2*k+1)/16**k for k in range(50)) 3.141592653589794 I've no idea what its name is or where it comes from, though. I expect Raymond Hettinger would know. -- Mark -- http://mail.python.org/mailman/listinfo/python-list
