Do ex 2.2 and 2.3

ex-2_01-xx.scm

@@ -53,3 +53,61 @@
 
 (display "\n\nex-2.2")
 
+(define (make-point x y) (cons x y))
+(define (x-point p) (car p))
+(define (y-point p) (cdr p))
+
+(define (make-segment a b) (cons a b))
+(define (start-segment s) (car s))
+(define (end-segment s) (cdr s))
+
+(define (midpoint-segment s)
+  (make-point (average (x-point (start-segment s)) (x-point (end-segment s)))
+              (average (y-point (start-segment s)) (y-point (end-segment s)))))
+
+(define (print-point p)
+  (newline)
+  (display "(")
+  (display (x-point p))
+  (display ", ")
+  (display (y-point p))
+  (display ")"))
+
+(define s (make-segment (make-point 1 2) (make-point 7 4)))
+(print-point (midpoint-segment s))
+
+(display "\n\nex-2.3\n")
+
+; The first representation takes the two opposite corners of the rectangle.
+(define (make-rectangle p1 p2) (cons p1 p2))
+(define (corner-1-rectangle r) (car r))
+(define (corner-2-rectangle r) (cdr r))
+
+(define (area-rectangle r)
+  (abs (* (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r)))
+          (- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r))))))
+
+(define (perimeter-rectangle r)
+  (* 2 (+ (abs (- (x-point (corner-1-rectangle r)) (x-point (corner-2-rectangle r))))
+          (abs (- (y-point (corner-1-rectangle r)) (y-point (corner-2-rectangle r)))))))
+
+(define r (make-rectangle (make-point -2 -2) (make-point -8 -10)))
+(display (area-rectangle r)) (newline)
+(display (perimeter-rectangle r)) (newline)
+
+; The second representation takes one corner and the size of the rectangle.
+; The consequence is that we have to calculate the second point for the
+; corner-2 getter.
+(define (make-rectangle p1 size) (cons p1 size))
+(define (corner-1-rectangle r) (car r))
+(define (corner-2-rectangle r)
+  (make-point (+ (x-point (car r)) (x-point (cdr r)))
+              (+ (y-point (car r)) (y-point (cdr r)))))
+
+; Our higher level functions still deliver the same result even though the
+; underlying presentation of the rectangle is different.
+(define r (make-rectangle (make-point -2 -2) (make-point -6 -8)))
+(display (area-rectangle r)) (newline)
+(display (perimeter-rectangle r)) (newline)
+
+(display "\nex-2.4\n")

util.scm

@@ -10,4 +10,6 @@
 (define (gcd a b)
   (if (= b 0) (abs a) (gcd b (remainder a b))))
 
+(define (average a b) (/ (+ a b) 2.0))
+
 ;(assert (gcd 93 15) 3)