Basic functions for working with continued fractions. These are handy for approximating irrational numbers as ratios of integer. A Fortran solution is available at https://fortran-lang.discourse.group/t/implmentation-of-contnued-fraction/124/2

continued_fractions.py

import math
from fractions import Fraction

def continued_fraction(r,steps=10):

	cf = []

	for step in range(steps):
		i = math.floor(r)
		cf.append(i)
		f = r - i
		if f == 0:
			break
		r = 1./f

	return cf

def contfrac_to_frac(seq):
    ''' Convert the simple continued fraction in `seq` 
        into a fraction, num / den
    '''
    num, den = 1, 0
    for u in reversed(seq):
        num, den = den + num*u, num
    return num, den

def main():

	r = (math.sqrt(3) + 1)/2
	print(r)
	for i in range(2,30):
		coeffs = continued_fraction(r,i)
		f = Fraction(*contfrac_to_frac(coeffs))
		print(f,float(f),float(f)-r)

	print(coeffs)

if __name__ == '__main__':
	main()