Approximate irrational numbers with a fraction

continued_fractions.py

https://en.wikipedia.org/wiki/Continued_fraction

from math import trunc, pi, sqrt

def approximate(alpha, iters):
    r = [alpha]
    a = []
    for i in range(iters):
        a.append(trunc(r[-1]))
        r.append(1/(r[-1] - a[-1]))
    P = [a[0], a[0]*a[1] + 1]
    Q = [1, a[1]]
    for i in range(2, iters):
        P.append(P[-1] * a[i] + P[-2])
        Q.append(Q[-1] * a[i] + Q[-2])
    return P[-1], Q[-1]

P, Q = approximate(sqrt(2), 5)
print("%d/%d = %f" % (P, Q, float(P)/Q))

P, Q = approximate(pi, 5)
print("%d/%d = %f" % (P, Q, float(P)/Q))