;; to draw a Sierpinski triangle down at a, b, and c,
;; assuming it is large enough
(define (sierpinski a b c depth)
  (cond
    [(= depth 0) true]
    [else 
      (local ((define a-b (mid-point a b))
	      (define b-c (mid-point b c))
	      (define c-a (mid-point a c)))
	(and
	  (draw-triangle a b c)	    
	  (sierpinski a a-b c-a (- depth 1))
	  (sierpinski b a-b b-c (- depth 1))
	  (sierpinski c c-a b-c (- depth 1))))]))

;; mid-point : posn posn  ->  posn
;; to compute the mid-point between a-posn and b-posn
(define (mid-point a-posn b-posn)
  (make-posn
    (mid (posn-x a-posn) (posn-x b-posn))
    (mid (posn-y a-posn) (posn-y b-posn))))

;; mid : number number  ->  number
;; to compute the average of x and y
(define (mid x y)
  (/ (+ x y) 2))

(define (draw-triangle a b c)
  (and
   (draw-solid-line a b 'black)
   (draw-solid-line b c 'black)
   (draw-solid-line c a 'black)))




;(define A (make-posn 200 0))
;(define B (make-posn 27 300))           -173,+300
;(define C (make-posn 373 300))          +173, 1 2 sqrt(5)

(define PI 3.141593)

(define top (make-posn 160 10))
(define side 300)
(define left (make-posn (- (posn-x top) (/ side 2))
                        (* (sin (/ PI 3)) side)))
                         
(define right (make-posn (+ (posn-x top) (/ side 2))
                         (* (sin (/ PI 3)) side)))
                       
(start 320 300)
(sierpinski top left right 10)