gistfile1.py

import sys
import math
import fractions


def pi_fraction(gap):
    """Print the fraction within gap of pi that has the smallest denominator.
    
    >>> pi_fraction(0.01)
    22 / 7 = 3.142857142857143
    >>> pi_fraction(1)
    3 / 1 = 3.0
    >>> pi_fraction(1.0/8)
    13 / 4 = 3.25
    >>> pi_fraction(1e-6)
    355 / 113 = 3.1415929203539825
    """

    denominator = 1
    numerator = 1

    while True:
        while float(numerator)/denominator < math.pi + gap:
            if abs(float(numerator)/denominator - math.pi) < gap:
                print "%d / %d = %f" % (numerator, denominator, float(numerator)/denominator)
                return
            numerator += 1
        denominator += 1
        numerator = denominator * 3