The **golden ratio** leads to fascinate mathematicians, painters and sculptors for hundreds of years. We find this in the math, nature, architecture, painting, and photography; and his name implies beauty, balance and harmony.

Through a series of mathematical calculations based on numeric set, you set the parameters of these proportions pleasing to the eye and applied since ancient times in all kinds of items that aspired to a formal perfection.

From the Parthenon to a photograph that follow the famous rule of thirds, a conch shell or the petals of a sunflower, the golden ratio present in so many things around us.

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## WHAT IS THE GOLDEN RATIO?

**The golden ratio is** the link between a series of numbers based on the golden number which is given to a cosmetic condition. What a form which respects the golden ratio is considered beautiful. The golden ratio has been applied with success in multiple projects, designs, buildings, photography, playing an important role in mathematics.

The golden ratio is also known as a reason golden mean, golden section or divine proportion.

The golden ratio is generated through a series of numerical known as a sequence (or series) of Fibonacci.

Fibonacci, also known as Leonardo of Pisa, was the famous mathematician who introduced the Arabic numerals in the west (until the time used the roman) and that broke the succession numerical infinite whose proportions approximate the golden number.

### WHAT IS THE FIBONACCI SERIES ?

The Fibonacci series is based on a succession of numbers infinite. Beginning with 1,1, the rest of the numbers are the sum of the previous two: 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13, 13+8=21 and so on until infinity.

If we divide each number in the Fibonacci series with the above, this value is approximated to the** golden number** , or number Phi, the value of which is 1,68033988749894…

If we do the division of the numbers of the Fibonacci series, we obtain results such as for example: 89/55= 1,61818182 or 144/89= 1,61797753, which as you can see correspond to the golden ratio, or Phi.

### WHAT IS THE GOLDEN NUMBER?

**The golden number is a number that is algebraic irrational** (their decimal representation is infinite and has no period) and is obtained from the relationship or ratio between two segments of a straight line, that is to say, of a geometric construction.

This value is the 1,618033988749894… and is obtained from the formula:

The golden number (or number Phi) was discovered in ancient times and has many interesting properties, since this ratio can be found in both figures arithmetic as in nature. It has often been related also with the divine.

In the video below what you have perfectly explained:

### THE SPIRAL-GOLDEN SPIRAL FIBONACCI

On A visual level, if we apply the Fibonacci numbers in a rectangle, we get a spiral with proportions as follows:

IF you look closely, you’ll see that the spiral golden ratio is a more complex version of the rule of thirds is applied in painting and photography.

## EXAMPLES OF GOLDEN RATIO

The golden ratio has fascinated me for hundreds of years all types of profiles, artistic or mathematical. Its proportions have been found in many natural elements, associated to perfection and the divine, has been applied in works of architecture, sculpture and painting.

Let’s look at some examples where we can find these proportions related to the golden number or golden number.

### THE GOLDEN RATIO IN NATURE

This golden ratio is very present in nature. It is especially interesting, for example, to analyze the petals of a sunflower, where the Fibonacci series is repeated to perfection.

In sunflowers, the first row of petals can contain 21, 34, 55 or 89 petals line in the second row, with 34, 55, 89, or 144. They are all numbers and proportions that are consistent with the Fibonacci numbers or the golden ratio.

And not only in the sunflowers we find this pattern, also in petals of different flowers (there are flowers with 3, 5 and 8 leaves and also with 13, 21, 34, 55, 89 and 144), in the distribution of leaves on a stem, in the relationship between the veins of the leaves of the trees, in the amount of spirals of a pine cone, on the structure of hurricanes, in the relationship between the distance between the coils of the inside of a snail, in the arrangement of the galaxies, etc

### THE GOLDEN RATIO IN THE HUMAN BODY

The search of the perfect proportions in the human body is something usual in the story. Perhaps one of the studies of the proportions most iconic is that Leonardo da Vinci did in his famous “Vitruvian Man” .

Adolf Zeising also carried out extensive research about the golden ratio in nature, and later in the human body, which sets out in his work “New doctrine of the proportions of the human body”, which concludes that the golden ratio applies universally.

The golden ratio in the human body is found, for example, the distance between the navel and the soles of the feet of a person with regard to his full height; the relationship between head length and width; in the relationship between the phalanges of the fingers, etc

If you look at, for example, one ear you will see that it is perfectly fulfils the spiral of the Fibonacci series.

### THE GOLDEN RATIO IN ART

The properties of the golden number or the golden ratio have been exploited in all branches of art since Antiquity due to its aesthetic character and his relationship with the beautiful, the mystical and divine.

Paintings such as the mona lisa or the last supper; the great Leonardo da Vinci; or the Meninas of Velázquez, fit to perfection in the golden ratio; also, the sculptures of Fídias, or compositions of musicians such as Debussy and Mozart.

Today you can find it applied in the design, posters or photography, always looking for the proportions of what is beautiful and pleasing to the viewer.

### THE GOLDEN RATIO IN PHOTOGRAPHY

In photography, the golden ratio is used to compose images aesthetically pleasing, balanced, and above all, to place the protagonist in specific points of the image where this stands out in a natural way.

The famous rule of thirds is a simplified version of this series of Fibonacci or golden ratio, and shows us the strong points of the image, which is reflected in the place where it is most easily emphasis the subject.

To split the frame in two horizontal and two vertical lines, creating 4 intersections. These intersections are the ones that we know as the strengths.

### THE GOLDEN RATIO IN ARCHITECTURE

Phidias, which is attributed to the conception of the temple Parthenon, as well as some of the finest sculptures of the Old, was a great enthusiast of the number of gold (in fact the name Phi is in honor of him).

Works such as the Parthenon, which aims to unite the beauty with the mystical, and his sculptures (conserved or not) is based on the golden number and the golden ratio.

We can also find the golden mean in architectural works such as the Great Pyramid of Giza or modern architects as famous as Mies Van der Rohe or Le Corbusier.

In short, the golden ratio is a way to get closer to the beauty of universal form. What are mathematically most closely approximates Phi, what we will perceive it as beautiful and perfect.

In photography, the spiral of the golden ratio, it can help us to compose a picture pleasing to the eye, as well as to set the place on which to place our protagonist.

But this notion of beauty and perfection is applicable both to architecture, as in painting, to music, to people or to the natural elements.

If you found it interesting, do me a favor and share this content with those who believe that you go to take advantage of it. Thank you very much and until the next.