Odds are that if you have been exploring with your Nikon or on vacation with your Canon you didn't bother to use the Fibonacci spiral or golden ratio to assist in your photography. However, without knowing it, you may have indeed used the timeless art of dynamic composition and visual tension. What you may not have realized is that the art of photography can be enhanced by the science of mathematics and ratios.
This all dates back to a long time ago with a guy named Fibonacci. And since I am neither a history major nor an aspiring "buff" I will spare you the details. The gist is explained by several great articles on both the Fibonacci ratio and the underlying rule of thirds here, here, andhere.
Take a quick look through them if you have a chance to explain the theory behind this compositional cheat sheet. I know that with my most recent iPhone I have turned the grid feature on to aid in the exact ways that these articles suggest.
Something to consider the next time you marvel at a beautiful photograph or Facebook profile picture.