Square root (method by Hal Abelson in SICP MIT course) - Python and Scheme version.

sqrt.py

def average(v1, v2):
    return (v1 + v2) / 2.0

def square(n):
    return n * n

def sqrt(n):
    def improve(guess):
	return average(guess, n / guess)
    def good_enough(guess):
	return abs(square(guess) - n) < 0.00000000001
    def tryit(guess):
	if good_enough(guess):
	    return guess
	else:
            return tryit(improve(guess))
    return tryit(1)

sqrt.ss

(define average (lambda (v1 v2) (/ (+ v1 v2) 2)))

(define square (lambda (n) (* n n)))

(define (sqrt n)
  (define (improve guess)
     (average guess (/ n guess)))
  (define (good-enough? guess)
     (< (abs (- (square guess) n)) 0.0000000001))
  (define (tryit guess)
     (if (good-enough? guess)
        guess
        (tryit (improve guess))))
  (tryit 1))