Matt Bowcock // mbowcock.com

Working my way through SICP has a goal I’ve had for a while but never seemed to get to.  However – this past week I started reading the book and working on the exercises and am looking forward to the challenge.  I skipped a couple of exercises in the first section but came up with the following to exercise 1.8:

(define (cube x)
  (* x x x))

(define (abs-val x)
  (cond ((> x 0) x)
    ((= x 0) 0)
    ((< x 0) (- x))))

(define (improve guess x)
  (/ (+ (/ x (* guess guess)) (* 2 guess)) 3))

(define (good-enough? guess x)
  (< (abs-val (- (cube guess) x)) 0.001))

(define (cube-root-iter guess x)
  (if (good-enough? guess x)
    guess
    (cube-root-iter (improve guess x) x)))

(define (cube-root x)
  (cube-root-iter 1.0 x))

Along with the exercises in SICP I plan to also apply my new found knowledge to some of the problems from Project Euler.  The solution I came up with for exercise 1 was probably overkill but it worked and should work for larger sets of numbers:

(define (calc-iter total count limit)
  (if (= count limit)
    total
    (calc-iter
        (+ (if (or (= (modulo count 3) 0) (= (modulo count 5) 0)) count 0) total)
        (+ count 1)
        limit)))

(define (calc x)
  (calc-iter 0 0 x))

(calc 1000)