Here are a couple of things you might have seen before.
How on earth do these things work. And what do they have in common?
More missing square puzzles. (My favourite is the one right at the bottom with the rotating pieces.)
Here is a fantastic video explaining these things from a former colleague of mine in Australia who is now a youtube star - as far as you can be one with math :)
Try to understand as many aspects of this as you can. Especially how the Fibonacci sequence is useful in constructing these things.