Some argue that the rule of thirds is simply a simplification of an even more advanced mathematical equation known as the golden ratio (also known as the golden mean). The golden ratio is a ratio which has continued to surprise artists, scientists, musicians and mathematicians for centuries. The reason being is that the golden ratio seems to pop up everywhere. Not only does the golden ratio pop up in everywhere, it also seems that the human eye is very attracted to the results of the ratio.
For example, there are certain measurements on models faces which equal surprisingly close to the golden ratio. In nature we see the golden ratio in plants and the branching of trees, the spirals of shells, the curves of waves, in our DNA and the solar system. It has also been used in architecture, art and music. The golden ratio seems to be everywhere.
It was used in architectural masterpieces such as the Greek Parthenon, the pyramids and later in such great works of art such as Notre Dame. There is also cause to believe that it was used by the great artists Michelangelo and Leonardo De Vinci.
It is debated as to whether the Mona Lisa was intentionally created using the proportions of the golden ratio. See below
A golden rectangle is a rectangle whose side lengths are in the golden ratio.
Simply put, the golden ratio is a ratio of approximately 1.618 to 1. This proportion creates a sense of harmony and balance.
Although this ratio has been rediscovered throughout time, one undisputed milestone in its history was the Fibonacci number series. In the 12th century Fibonacci produced a series of numbers by adding together pairs of numbers.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
(0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8)
The ratio between each successive pair gets closer and closer to Phi as you progress through the series.
Once you start splitting a golden rectangle by the ratio, you can keep sub-splitting it down forever. The spiral this produces exactly matches the growth of the Nautilus shell in nature. Yes, it's all getting a little freaky now.
Let's just say it's a mathematical equation of aesthetically pleasing composition.
Below see how Cartier-Bresson used the proportions of the Golden Rectangle to form his composition.
Remarkably this pattern also shows up in nature:
Here is a video on the Golden Ratio subject:
How to Get the Golden Ratio To Appear In Adobe Lightroom:
Did you know you can even turn on a golden ratio overlay in Adobe Lightroom when you're cropping?
It looks like this:
Just type the O key when you are cropping an image. Keep tapping the O key until you see your golden ratio. O as in the letter not the number. How handy is that?!
Also keep hitting O key and it will cycle through the various cropping guides. Another tip is to hit Shift-O and your golden ratio cropping guide will change location. Just keep hitting Shift-O and Adobe Lightroom will cycle through all your choices.
Finally I had to put this here because I think it's hilarious: