#!/usr/bin/env python

import math

def get_cont_fractions (p, maxlen=10):
   c_fract = []
   while len (c_fract) < maxlen:
      c = int (math.floor (p))
      c_fract.append (c)
      d = (p - c)
      if math.fabs (d) <= 0.00000001:
         break;

      p = 1.0 / d

   return c_fract


def get_frac_from_cont_fractions (c_fract):
   if not c_fract:
      raise "Empty List as Continuos Fractions"

   c_f = c_fract[:]
   c_f.reverse ()
   a, b = 0, 1
   for i in c_f:
      a, b = b, i * b + a

   return b, a
      
   
   
p = 1.0

for i in range (10):
   p *= 1.0 / (1 + math.sqrt (5.0)) * 2
   print "\n%.10f:" % p

   for n in range (4):
      cf = get_cont_fractions (p, n+1)
      a, b = get_frac_from_cont_fractions (cf)
      print "%d/%d = %.10f" % (a, b, float (a) / b)