The code below incorporates the newly revised python 3.3.0 decimal module to permit arbitrary precision (http://docs.python.org/3/library/decimal.html)
The recipe was originally by FB35 from http://code.activestate.com/recipes/576981-archimedes-method-for-calculating-pi/
Python, 33 lines
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | # Archimedes Method for PI
# FB - 200912082
# Revised by Bjorn.madsen AT operationsresearchgroup.com for Python3.3
# BHM - 20130302
import decimal
def ArchPi(precision=99):
# x: circumference of the circumscribed (outside) regular polygon
# y: circumference of the inscribed (inside) regular polygon
decimal.getcontext().prec = precision+1
D=decimal.Decimal
# max error allowed
eps = D(1)/D(10**precision)
# initialize w/ square
x = D(4)
y = D(2)*D(2).sqrt()
ctr = D(0)
while x-y > eps:
xnew = 2*x*y/(x+y)
y = D(xnew*y).sqrt()
x = xnew
ctr += 1
return str((x+y)/D(2))
if __name__ == '__main__':
print(ArchPi(99))
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Pi with 1024 decimals: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632812