Rise to the equation

In 1200 AD an Italian noticed that plants grow from the ground in a certain way. He observed that when the shoot pushed from the soil it created the stem first. Soon after appeared the first leaves and branches. It looked like this:

Plant

The man was called Leonardo Pisano and he lived in Pisa. Today though, he is remembered at Leonardo Fibonacci from filius Bonacci, which means “the son of Bonaccio”. Simply by observing nature, he rediscovered the long lost creation sequence:

1,1,2,3,5,8,13,21,34,55,89,144…

Pythagoras called this God BREATHING ON THE NUMBERS, but today it is simply referred to as the Fibonacci sequence. The Fibonacci sequence is neither arithmetic (based on the addition of numbers by a constant: 1, 2, 3, 4…) nor geometric (based on the multiplication of numbers by a constant: 2, 4, 6, 8…) but instead recursive. A recursive sequence is based on the addition of two adjacent numbers to produce a third: 1, 1, 2, 3, 5, 8, 13…If we wished to express this sequence as an equation it would look like:

x + 1 = x²

Solving for x using the quadratic equation we get x = 1.618. When using this number we denote it as Φ and refer to it as Phi in commemoration of the Greek sculptor Phidias.

We call this relationship the GOLDEN RATIO or 1:1.618.