THE GOLDEN RATIO
Floor 3“The geometry has two great treasures: one is the Pythagorean theorem; the other is the division of one line according to the extreme and middle relationship. We can compare the first to a certain amount of gold, and define the second precious stone”
The golden is a number (1,618...) that derives from the geometric proportion discovered by the Pythagoreans, defined by Euclide, called, in a treatise by Luca Pacioli illustrated by Leonardo, divine proportion and later, in the denteenth century, golden.
It is an irrational number, that is, it cannot be expressed with a fraction and has infinite decimal digits without repetitive sequences.
This particular issue occurs with incredible frequency in nature and in the cosmos, architecture, sculpture, music and appears as a symbol of the harmony of the universe and wherever the beauty comes from the harmony of proportions is recognized.
AC / CB = AB / AC
Euclide, in the Book VI of Elements, defines the golden ratio or extreme and average proportion: “a straight line is divided according to the extreme and average proportion when the whole line stands at the greater part as the greater is at the lower.”
A property of the golden ratio is that such division gives rise to a process that can be repeated to infinity: from an aureous segment we can get infinite sections auree ever smaller.
1/1 = 1,000000
2/1 = 2,000000
3/2 = 1,500000
5/3 = 1,666666
8/5 = 1,600000
13/8 = 1,625000
21/13 = 1,615385
34/21 = 1,619048
55/34 = 1,617647
89/55 = 1,618182
144/89 = 1,617978
233/144 = 1,618056
377/233 = 1,618026
610/377 = 1,618037
987/610 = 1,618033
In close relationship with the divine relationship lies the succession of Fibonacci, numerical series in which the relationships between the terms approach quickly to that of the golden ratio.
