some solutions for MIT Press's "structure and interpretation of computer programs", I guess
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 `(define (square x)` ` (* x x))` `(define tolerance 0.00001)` `(define (fixed-point f first-guess)` ` (define (close-enough? v1 v2)` ` (< (abs (- v1 v2))` ` tolerance))` ` (define (try guess)` ` (let ((next (f guess)))` ` (if (close-enough? guess next)` ` next` ` (try next))))` ` (try first-guess))` `(define (average x y)` ` (/ (+ x y) 2))` `(define (average-damp f)` ` (lambda (x) (average x (f x))))` `;(define (nice-sqrt x)` `; (fixed-point (average-damp (lambda (y) (/ x y)))` `; 1.0))` `(define (cube-root x)` ` (fixed-point (average-damp (lambda (y) (/ x (square y))))` ` 1.0))` `(define dx 0.00001)` `(define (deriv g)` ` (lambda (x) (/ (- (g (+ x dx)) (g x)) dx)))` `(define (cube x)` ` (* x x x))` `(define (newton-transform g)` ` (lambda (x) (- x (/ (g x) ((deriv g) x)))))` `(define (newtons-method g guess)` ` (fixed-point (newton-transform g) guess))` `;(define (nice-sqrt x)` `; (newtons-method` `; (lambda (y) (- (square y) x)) 1.0))` `(define (fixed-point-of-transform g transform guess)` ` (fixed-point (transform g) guess))` `(define (nice-sqrt x)` ` (fixed-point-of-transform` ``` (lambda (y) (- (square y) x)) newton-transform 1.0)) ``` ``` ```