sicp1.3 发现一个计算 Π 的方法

simple_pi.scm

(define (sum term a next b)
    (if (> a b)
        0
        (+ (term a)
           (sum term (next a) next b)
        )
    )
)

; 结果逼近 Π/8
(define (pi-sum a b)
    (define (pi-term x)
        (/ 1.0 (* x (+ x 2)))
    )

    (define (pi-next x)
        (+ x 4)
    )

    (sum pi-term a pi-next b)
)

(define (my-pi n)
    (* 8 (pi-sum 1 n))
)
#|
> (my-pi 10)
2.976046176046176
> (my-pi 10)
2.976046176046176
> (my-pi 100)
3.1215946525910105
> (my-pi 1000)
3.139592655589783
> (my-pi 10000)
3.141392653591793
> (my-pi 100000)
3.141572653589795
|#