Add notes for 3.27

notes.txt

@@ -116,3 +116,18 @@ For z as in the example,
 (sqrt (+ (square 3) (square 4)))
 5
 
+
+3.27
+
+For i = 0 or 1, (memo-fib i) is O(1). For i > 1, it is n additions.  This is because
+for each i, (memo-fib i) is only calculated once.  This calculation is O(n) and each subsequent
+lookup is O(1).  So, even though (memo-fib i) is called multiple times for each i, only i additions are
+done for each.
+
+This scheme will not work if we use (define memo-fib (memoize fib)).  The fib procedure is
+defined recursively in terms of itself, and each of the these recursive calls will be evaluated in
+an environment whose enclosing environment is the global environment.  This explicitly does not include
+the table of pre calculated results, so we will not get the benefit of this.  Defining memo-fib recursively
+in terms of itself means that the recursive calls are evaluated in an environment whose enclosing
+environment is one where memoize has been evaluated, and thus it contains the table.  This is critical
+to make the memoization work as required.