Visual Thinking Research

-How many triangles can you find in this picture?
      A friend and I sat down to try to solve this visual problem. Initially, we both started with a top down analysis of the picture. Staring at the top, we worked ourselves down, making sure not to miss anything. We counted out how many triangles that we found, 16. After looking over the cat again, we were sure that our answer was correct. What my friend and I had failed to take into account was the combination of triangles that also formed triangles themselves. The final answer was 20.
http://www.puzzles.com/PuzzlePlayground/Cat/Cat.htm

- Count how many perfect squares of all possible sizes are hidden in the cross of dots above. A square is counting if any four dots are placed exactly in its respective corners.
       With the same friend from the previous visual test, we sat down to try to conquer another. We employed the same technique as the first puzzle, top down visualization. After that process, we both had tried to find more squares, knowing that there would be more. What we had failed to do was to find more squares by looking at the cross of dots from an angle. Initially we found 9 squares. After looking at the solution, we realized that there were 21 perfect squares. 
http://www.puzzles.com/PuzzlePlayground/HowManySquares/HowManySquares.htm