Reading through more SICP and I'm stuck on exercise 1.3.8. My code works properly for approximating 1/phi, but doesn't work for approximating e - 2.
(define (cont-frac n d k)
(define (frac n d k)
(if (= k 0)
1.0
(+ (d k) (/ (n (+ k 1)) (frac n d (- k 1))))))
(/ (n 1) (frac n d k)))
(define (eulers-e-2)
(cont-frac (lambda (i) 1.0)
(lambda (i)
(if (= (remainder (+ i 1) 3) 0)
(* 2.0 (/ (+ i 1) 3))
1.0))
100))
(define (1-over-phi)
(cont-frac (lambda (i) 1.0)
(lambda (i) 1.0)
100))
Instead of getting .7 blah blah blah for e-2, I'm getting .5 blah blah something. I can't figure out why. I'm pretty sure I have "d" defined properly in the "eulers-e-2" function.
Edit: Thanks guys, I was calculating it backwards. Here's the fixed code.
(define (cont-frac n d k)
(define (frac n d i)
(if (= k i)
(d i)
(+ (d i) (/ (n (+ i 1)) (frac n d (+ i 1))))))
(/ (n 1) (frac n d 1)))
You seem to be calculating the following:
N1/(D100 + (N101/ D99 + N100/(D98 + N99/(..))))
Instead of
N1/(D1 + N2/(D2 + ...))
Since N and D are the same (all 1s) for 1/phi, you get the right answer there.