Not much progress, but a little fun.

chapter1/src/chapter1/AnswerToExercise_1_14_(skipped).txt

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+An interesting thought challenge, but not the one I seek right now.
+
+So I skip this exercise.    

chapter1/src/chapter1/AnswerToExercise_1_15_calculating_π.clj

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+;;; a) Four times.
+;;; b) It grows with the logarithm of a.
+;;
+;;; And now let's have some fun and calculate π !
+;;
+;; Well known mathematical background:
+;;
+;; Start with a value of 3 (or any positive number
+;; less than 2π) as your initial guess g_0 for π.
+;;
+;; To obtain the new guess g_(n+1), simply add
+;; sin(g_n) of the previous guess g_n to g_n.
+;;
+;; This produces a sequence that approximates π.
+;;
+;; Quite rapidly indeed:
+;; When the guess is already quite close,
+;; so it the first N digits are correct already,
+;; adding sin will result in a value
+;; that has the first 3*N digits correct
+;; (approximately; the higher N is to start with, the better).
+;;
+;; When the initial guess is anything positive below π,
+;; all other guesses will be below π as well.
+;;
+;; When the inital guess is anywhere
+;; between π and strictly smaller than 2π,
+;; all other guesses will be above π as well.
+;;
+;; This is not a very practical method to calculate π,
+;; as it is computationally rather expensive to
+;; compute sin(x) if x is near π .
+;;
+;; While it may be expensive, as exercise 1.15 shows,
+;; it can be done (without prior knowledge of π).
+;;
+;; Exercise 1.15 gives us a sequence of approximative
+;; functions sin_n, that approximate sin.
+;;
+;; One could try something like the straightforward iteration
+;;
+;; h_0 = 3
+;; h_(n+1) = h_n + sin_n(h_n)
+;;
+;; This does not work very well at first,
+;; as sin_0(3) = 3, so h_1 comes out as 6.
+;;
+;; So let us instead use
+;;
+;; h_(n+a) = h_n + sin_(n+3)(h_n).
+
+(defn sin_n[n x]
+  "n-th approximation of sin"
+  (defn div_x_3**n [x three**k n-k] ; first multiply 3**n, I think this gives better precision.
+    (if (= n-k 0) (/ x three**k)
+      (recur x (* three**k 3) (- n-k 1))))
+  (defn repeat_p_n_times [x n]
+    (if (= n 0) x
+      (recur (- (* 3 x) (* x x x 4)) (- n 1))))
+  (repeat_p_n_times (div_x_3**n x 1.0 n) n))
+
+(defn guesses_for_π []
+  "generate an infinite sequence of guesses for π"
+  (defn h_tail [h_n n+3]
+    (lazy-seq (cons h_n (h_tail (+ h_n (sin_n (+ n+3 1) h_n)) (+ 1 n+3)))))
+  (h_tail 3.0 3))
+
+(defn prn_first_n_guesses [n]
+  "prn the first n guesses for π."
+  (
+    (fn show [n s ignore]
+      (if (seq s) (recur (+ n 1) (rest s) (prn n (first s)))))
+    0 (take n (guesses_for_π)) nil))
+