Although not always consciously, when designing a poster, website, diptych, we adopt a picture composition. I say that not always consciously, or perhaps one should say premeditated, because in many cases the material available is the one who leads the design to a type of composition or other impulse depriving print designer to design aesthetics, beauty and emotion. In a future publication I’ll go deep more into the image composition techniques.

One of the many ways to achieve aesthetic and balanced compositions is recourse to the **golden ratio**, also known as **golden section**. This type of composition can be easily achieved without resorting to calculators, square, bevel and compasses. But first let me try to describe what is the golden ratio to make it easier to understand the composition process using this technique.

First time I heard the term golden ratio I thought they were talking about some formula by Paracelsus, one of the most famous alchemists. I could not have been more wrong … My first real contact with the term was by design treaties where is mentioned as having the property to get beautiful proportions and pleasing to the eye.

Stripped of all mysticism the golden ratio, is now known by the Greek letter **Fi (Φ)** in honor Fideas, the most famous sculptor of ancient Greece. Its value is expressed by the following formula:

Φ = (1+√5) / 2 ≈ 1,61803398874...

The first man to state the existence of the golden proportion between segments of a line was Euclid (300-265 a. C.). This proportion is present in many geometric shapes, engineering, you can perceive their constant presence in the plant world and has been used in different forms of art such as architecture, painting or music.

To find the auric point of a line *C* simply proceed to divide its value by the golden number, or you can follow the geometric model that you see below.

There are many other formulas associated with the golden ratio that will delight all those who you passionate about mathematics. Later on you can find in the links section some web pages which displays such formulas. In either way you get the same result, Auric point divides the line into two segments *A* and *B* that are in golden ratio. Moreover according to the definition of *Euclid*:

“It is said that a straight line is divided between the end and proportional when the whole line is to the greater segment as the largest is at the lowest.”

The straight segment *A* and *C* are also golden ratio.

The next logical step to design using this ratio is to create a auric rectangle. Like in the case of the line is possible there is no single method to get a rectangle that has a golden proportions, but the two methods that I will detail below are equally simple. Right based on a square squares are added showing how the image from the third square form golden rectangles that hold the golden ratio to one another. In the second method, to the left of dividing one forming a right triangle legs taking as half of one side CD / 2 and the adjacent side BD. The resulting hypotenuse side will allow us to draw a new rectangle BEFD which together with the previous square ABDC form a AEFC the golden rectangle. The two new rectangles are golden and also achieved are in golden ratio. From these rectágulos can build templates for composing simple designs like the one you can download from here to design web pages.

If you look closely the golden rectangle on the right is the next series on their sides:

0 + 1 = 1 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 8 + 13 = 21 13 + 21 = 34 21 + 34 = 55 ....

This numerical progression is called the **Fibonacci series** as *Johannes Kepler* discovered in the sixteenth century is deeply attached to the golden ratio. Each issue of the series has been in approximately golden ratio with the previous number, the higher the numeral is closest to the number Φ. In addition, this rectangle built with the Fibonacci series can quickly turn into a **(pseudo) golden spiral** straight arcing within the squares as follows.

What use is all this? As I have said before **it is very easy to build a grid design from golden rectangle**, no matter which of the methods was used to form it. The golden spiral offers many possibilities, apart from the merely aesthetic, can serve perfectly to **quickly get the most golden landmark of a document and expansion areas that point**. The golden ratio to create asymmetrical designs whose beauty is more subtle and easier to grasp by the human eye than symmetrical compositions. The rule of thirds is used exactly to do the same.

The template shown below is one of the easiest to do. But simply providing the design in this way will make it much easier to assimilate to an observer intuitively.

The understanding of the golden ratio will change the way you see the objects around you, for example, objects could be psychologically obvious negative connotations such as credit cards or packets of snuff, are golden rectangles as this gives them a certain aesthetic beauty, that’s called marketing …

To quickly see if an object maintains golden proportions just put side by side, along the short side and long side to draw a diagonal from the top and bottom corners of the assembly, if three vertices are aligned is that the golden ratio is fulfilled in that object.

A&8s

Links:

- Complete information of the auric number en.wikipedia.org
- The golden ratio by Eric W. Weisstein mathworld.wolfram.com
- Art and applications of Phi goldennumber.net

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