The Golden Ratio.

Also known as the Divine Proportion, The Golden Mean, or Golden Section, is a number that plays a major role in architecture, art, the way we perceive beauty and is found freely in the natural designs of various life forms.
It is basically viewed as an irrational mathematical constant and equals approximately 1.6180339887. It is often labeled Phi.

The number itself was determined by a mathematical calculation of a sequence of numbers, called the Fibonacci sequence.
Leonardo Fibonacci was born around AD 1170 and was an Italian mathematician, considered by some as the most talented mathematician of the Middle Ages.

As with anything mysthical and unusual, I am utterly intrigued by the Golden Ratio. Still, even though I have researched the subject in depth I feel I am not an expert yet to adequately explain the mathematics and the theory behind the ratio. This can be much better achieved by reading the numerous sites online dedicated to this enchanted number, such as this one. Some list objects, designed by the Golden Mean and truly, when looking at them, they do appeal to be more beautiful and eastethic, when compared to those that are not designed with the ratio in mind.

Both Leonardo Da Vinci and Sandro Botticelli created paintings that seem to follow the law of the Divine Proportion. Today, many artists and designers are very aware of it's existence and use it avidly in their work. The principles of the sequence can also be found in other areas, not just art and architecture. The Golden Mean is obvious in music, photography, interior design, graphic design and even in nature.
Some examples are: Da Vinci's Mona Lisa and The Last Supper (art), the Greek Parthenon and Egyptian Pyramids (architecture), the design of a Nautilus Shell (nature) and in the masterpieces of numerous composers such as Bartók, Debussy, Schubert, Bach and Satie.

I found particularly this animation very helpful when understanding how the formula is used in praxis and the clip below examins the Golden Ratio even more in depth.