Exercise1-37 <---> Exercise1-39

Exercise 1.38

In 1737, the Swiss mathematician Leonhard Euler published a memoir De Fractionibus Continuis, which included a continued fraction expansion for e - 2, where e is the base of the natural logarithms. In this fraction, the N_i are all 1, and the D_i are successively 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, .... Write a program that uses your cont-frac procedure from exercise 1.37 to approximate e, based on Euler's expansion.

Scheme solution:

(define (euler k)
  (define (d i)
    (if (= (modulo (1+ i) 3) 0)
        (* (/ (1+ i) 3) 2.0)
        1.0))
  (+ 2.0 (cont-frac (lambda (i) 1.0) d k)))

Haskell solution:

euler k = 2 + cont'frac (const 1) d k
  where d i | (i+1) `mod` 3 == 0 = 2 * fromIntegral (i+1) / 3
            | otherwise          = 1

Exercise1-37 <---> Exercise1-39

Comments

As I see it this is a perfect time to use "let"... The solutions are the same of course. (define (euler x) (define (d i) (let ((index (/ (+ i 1) 3))) (if (integer? index) (* 2 index) 1))) (+ 2.0 (cont-frac (lambda (i) 1) d x)))

Posted by DanielMoerner at 2008-12-25 07:35:21

Add your comment Markup