2 files changed, 13 insertions, 1 deletions
diff --git a/ex/2/50.rkt b/ex/2/50.rkt
index 3a67578..70c23db 100644
--- a/ex/2/50.rkt
+++ b/ex/2/50.rkt
@@ -2,7 +2,10 @@
 
 #lang racket
 
-(provide transform-painter)
+(provide
+ transform-painter
+ counterclockwise-180
+ counterclockwise-270)
 
 (require "46.rkt")
 (require "47.rkt")
diff --git a/ex/2/51.rkt b/ex/2/51.rkt
index 975c064..8f28d76 100644
--- a/ex/2/51.rkt
+++ b/ex/2/51.rkt
@@ -43,3 +43,12 @@
       (lambda (frame)
         (paint-above frame)
         (paint-below frame)))))
+
+
+;;; below in terms of rotate operations
+(define (below-rot painter1 painter2)
+  (let ((painter1-270 (counterclockwise-270 painter1))
+        (painter2-270 (counterclockwise-270 painter2)))
+    (counterclockwise-270
+     (counterclockwise-180
+      (beside painter1-270 painter2-270)))))