2 days ago
my attempt to do the exercises in sicp.
Tuesday, July 1, 2008
sicp exercise 1.38
; 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 Ni are all 1, and the Di 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.
(define (cont-frac-iter n d k)
(define (iter i result)
(if (= i 0)
(iter (- i 1) (/ (n i) (+ (d i) result)))))
(iter k 0))
(define (ones i) 1)
(define (double i) (* i 2))
(define (scale proc n factor def)
(if (= (remainder (+ n 1) factor) 0)
(proc (quotient (+ n 1) factor))
(define (d n) (scale double n 3 ones))
(display (cont-frac-iter (lambda(i) 1.0) d 1000))(newline)
; Answer: 0.718281828459045