def root_finder(a, b, tol, f):
    """ a, b are real numbers, a < b. tol > 0, f is a real-valued
    continuous function defined on [a,b] that changes sign."""
    while b - a > 2*tol:
        m = (a + b)/2.0
        print(a, b, m)
        if f(a)*f(m) < 0:
            b = m
        elif f(m)*f(b) < 0:
            a = m
        else:
            return m
    return m 

print(root_finder(1, 2, .0001, lambda x:x*x - 2))
print(2**(.5))
print(root_finder(4, 5, .0001, lambda x:x**3 - 100))