Phi, the golden section or golden ratio, famous throughout history has been and is for many a symbol of beauty, magic, perfection, divinity, ... in this post I will tell you all about it. 
To start a very simple practice, get a credit card or your ID card, a card, a passport photo ... and divide the length by the width, as you will see almost always ratio is a number close to 1.618 ... Not incidentally, this is the number of gold since ancient times has been considered the ideal length-width ratio (golden ratio), therefore, that many objects are currently Rigano by it. But one thing, algebraically, if we solve the following equation:
x 2 = x +1
we all terms aside,
x 2-x-1 = 0
and resolve, is:
Taking the positive solution, we obtain:
and resolve, is:
Taking the positive solution, we obtain:
This irrational number (infinite nonperiodic decimal) is known as the golden number, briefly, Phi, in honor the sculptor Phidias, who both used it, is represented by the letter Greek, which is the initial Phidias Greek.
This number is so famous, because from ancient Greece, through Roman, Renaissance and coming artists to painters, sculptors, architects, ... current has been considered the ideal proportion and canon of beauty, so they have used for multiple buildings and works of art ... But he also noted the presence of this in nature, geometry, etc..
The Parthenon in Athens, is a clear example of construction in which we can find the famous golden rectangle in different parts. Another example construction that follows is why is the cathedral of Notre Dame de Paris, see photo.
Surprised?, Because there's more, the great Renaissance painters, and knew this 
secret, say for example Leonardo da Vinci and his famous Gioconda, yes, the box most famous in the world, was painted by the rules of this magic rectangle, another of his works, the famous Vitruvian Man also follows that proportion, in fact believed that a person was mathematically perfect if its height and distance from floor to navel were golden ratio ... I know, not everyone can be mathematically perfect, but almost, try it and see that you approach quite the number.
The number of gold is closely linked to the regular pentagon and pentagram (a symbol of the school of Pythagoras, and also knew him then), because the ratio AD / AB gives again as a result the number of gold in the photo, we can appreciate in The Holy Family by Michelangelo.
He commented by the presence also of this proportion in nature, one of the most beautiful and best known is the case of Nautilus (coiled snail), hence known as golden spiral.
In a previous post I talked about the close relationship between the number of gold and the Fibonacci sequence, both present in many natural phenomena, eg Sunflowers have two sets of spirals that leave the center (one in each direction), 21 in one direction and 34 in the other, numbers that are extracted the famous series.
Coincidence?. No, mathematics, and that nature is wise. According're making the ratios of the terms of the Fibonacci sequence, you'll notice that every time is closer and closer to the golden number. Anecdotes and examples and there are thousands and I are leaving a post as long and do not want to be heavy, just say that this proportion is still used today, was considered ideal, as I mentioned before, our ID is famous golden ratio.
You see, the number of gold still present in our latest art, our late genius Salvador Dalí, for example, used it for some of his works and will be continued in future generations, to be considered a magic number.
I leave you with a couple of videos that will inform you more about this fascinating number.
This number is so famous, because from ancient Greece, through Roman, Renaissance and coming artists to painters, sculptors, architects, ... current has been considered the ideal proportion and canon of beauty, so they have used for multiple buildings and works of art ... But he also noted the presence of this in nature, geometry, etc.. 
The Parthenon in Athens, is a clear example of construction in which we can find the famous golden rectangle in different parts. Another example construction that follows is why is the cathedral of Notre Dame de Paris, see photo. 
Surprised?, Because there's more, the great Renaissance painters, and knew this 
secret, say for example Leonardo da Vinci and his famous Gioconda, yes, the box most famous in the world, was painted by the rules of this magic rectangle, another of his works, the famous Vitruvian Man also follows that proportion, in fact believed that a person was mathematically perfect if its height and distance from floor to navel were golden ratio ... I know, not everyone can be mathematically perfect, but almost, try it and see that you approach quite the number. 
The number of gold is closely linked to the regular pentagon and pentagram (a symbol of the school of Pythagoras, and also knew him then), because the ratio AD / AB gives again as a result the number of gold in the photo, we can appreciate in The Holy Family by Michelangelo. 
He commented by the presence also of this proportion in nature, one of the most beautiful and best known is the case of Nautilus (coiled snail), hence known as golden spiral. 
In a previous post I talked about the close relationship between the number of gold and the Fibonacci sequence, both present in many natural phenomena, eg Sunflowers have two sets of spirals that leave the center (one in each direction), 21 in one direction and 34 in the other, numbers that are extracted the famous series. 
Coincidence?. No, mathematics, and that nature is wise. According're making the ratios of the terms of the Fibonacci sequence, you'll notice that every time is closer and closer to the golden number. Anecdotes and examples and there are thousands and I are leaving a post as long and do not want to be heavy, just say that this proportion is still used today, was considered ideal, as I mentioned before, our ID is famous golden ratio. 
You see, the number of gold still present in our latest art, our late genius Salvador Dalí, for example, used it for some of his works and will be continued in future generations, to be considered a magic number. 
I leave you with a couple of videos that will inform you more about this fascinating number. 
