Square root calculator with Recursion.

approximation_algorithm.py

def next_(n, x):
    return (x + n / x) / 2

# Repeats infinitely
def repeat(f, a):
    yield a
    for v in repeat(f, f(a)):
        yield v

# Delimiter       
def within(ε, iterable):

    def head_tail(ε, a, iterable):
        b = next(iterable)
        if abs(a-b) <= ε: 
            return b
        return head_tail(ε, b, iterable)
    return head_tail(ε, next(iterable), iterable)
    
def sqrt(a0, ε, n):
    return within(ε, repeat(lambda x: next_(n,x), a0))


sqrt(1.0, .0001, 2) #Same as √2
sqrt(1.0, .0001, 3) #Same as √3