Added my solutions so far

ex-1-37.rkt

@@ -0,0 +1,42 @@
+#lang racket
+
+(define (cont-frac nf df k)
+  (define (recurse i)
+    (if (>= i k)
+        0
+        (/ (nf i) (+ (df i) (recurse (+ 1 i))))))
+  (recurse 0))
+
+; produces the same result as cont-frac, but
+; generates an iterative process.
+(define (cont-frac-iterative nf df k)
+  (define (iterate i numer denom)
+    (if (<= i 0)
+        (/ numer denom)
+        (iterate (- i 1) (nf (- i 1)) (+ (df (- i 1)) (/ numer denom)))))
+  (iterate (- k 1) (nf k) (df k)))
+
+(define (golden-ratio k)
+  "cont-frac generates 1/golden ratio, so we just inverse it to get the
+   real thing. call with k=1000 or something to get an accurate result"
+  (/ 1.0 (cont-frac-iterative (λ (i) 1.0) (λ (i) 1.0) k)))
+
+;; example 1-38
+(define (e-helper i)
+  (let ((r (remainder (- i 1) 3)))
+    (if (= 0 r)
+        (* 2.0 (/ (+ i 2) 3))
+        1.0)))
+(define (eulers-constant k)
+  "Finds euler's constant. the continued fraction gives e - 2, so we add 2."
+  (+ 2 (cont-frac-iterative (λ (i) 1.0) e-helper k)))
+
+;; example 1-39
+(define (tan-cf x k)
+  "Finds an approximation of the tangent function. The first numerator is not negative,
+   even though our numerator function calculates them all as negative, so we need to negate
+   the result at the end."
+  (-
+   (cont-frac-iterative (λ (i) (- (if (<= i 0) x (* x x))))
+                        (λ (i) (- (* 2 (+ i 1)) 1))
+                        k)))