The golden ratio is a number represented by the Greek letter “phi” that is formed when a line is divided into two parts, so that the smaller part divided by the longer part is equal to the entire length of the line divided by the longer part. Its represented as such:
a/b = (a+b)/a = 1.6180339887498948420 …
the Fibonacci sequence, discovered by Leonardo of Pisa, is directly linked to the Golden ratio. This is because when you calculate the ratio of two successive Fibonacci numbers the result gets closer to the Golden ratio. As the numbers grow, the result gets closer to 1.618.
This number can be applied into the composition of a rectangle, creating a shape called the Golden rectangle. It has been proven that humans have a psychological reaction towards this geometric form as it transmits visual satisfaction, for this reason it has been used in several works of art throughout the centuries.
Artists like Leonardo da Vinci have used the golden ratio to correctly place the compositions of the human figure within a portrait, in order to study the relationship between the anatomy and the mathematical geometry of the human body.
“Many books claim that if a rectangle is drawn around the face of the Louvre ‘Mona Lisa’, the ratio of the height to width of that rectangle is equal to the ‘Golden Ratio’.” http://monalisa.org/2012/09/12/leonardo-and-mathematics-in-his-paintings/
This shows us a direct link between the arts and mathematics. That geometry is not only applied to virtual shapes but also esthetic and symbolic arts, aside from paintings we can witness it also in architecture and sculpture.