A demonstration of Khinchin's constant for the continued fraction expansion of the number pi. Obviously as python has finite precision floating point, this is only an approximation, and is likely to approach an incorrect result as a grows larger.

Khinchin.py

#!/usr/bin/python3

from math import floor
from math import pi

def getExpansion(y):
  x = y
  while True:
    z = floor(x)
    yield z
    z = 1/(x-z)
      
def main(count=2000):
  x = pi
  r = getExpansion(x)
  acc = 1.0
  print("a_n\tgeo. mean")
  for a in range(1,count+1):
    rn = next(r)
    acc *= pow(rn,1/a)
    print("{}\t{}".format(rn,acc))
    acc = pow(acc,a/(a+1))

if __name__ == "__main__":
  if len(argv) > 1:
    main(int(argv[1]))
  else:
    main()