One of the entries subjects adapted to the geometry, group presents us “AG Los trapezoids”, where rescue basics of using multiple applications in engineering: The **golden ratio**.

This number, geometric relationship also, has been chosen as the theme for other groups of students because of its importance, both the basic study golden ratio (a good introduction simplified adding a funny video of Donald Duck) as in the proportions of the human figures,

I leave therefore analysis of this relationship, delving into some interesting concepts.

## by AG Los trapezoids

The** golden ratio or gold** (also called

*number dorado*,

*golden ratio*,

*golden ratio*,

*golden mean*,

*golden ratio*and

*divine proportion*) represented by the Greek letter

**(be) (to honor the Greek sculptor Phidias), is the irrational number:**

*F*This is an algebraic number that has many interesting properties and was discovered in antiquity, not as "unit" of measure, but as *relationship* or *proportion* between segments.

This ratio is found both in some shapes and elements in nature such as shells, ribbing tree leaves, the thickness of the branches, etc..

Also, is attributed *aesthetic* special objects that follow the golden ratio, and mystical significance. Throughout history, importance has been given in various works of architecture and other arts, although some of these cases have been objectionable for mathematics and archeology.

This divine proportion can be expressed easily in words:

"THE RELATIONSHIP WITH KEEPING ALL SHARE MORE , IS THE SAME AS THE MAJOR PART OF THIS PART WITH LESS THAN IS COMPLEMENTARY TO ALL ".

When a segment is divided into two parts, so that the reasons given above the number "fi" , is said, in the words of Euclid, that this segment has been*cut in extreme and mean ratio*.

Apparently, harmony which entails that all keep this relationship with its parts is inherent to human perception, that not only is able to detect an innate, but also thank her.

Is there, perhaps, some secret code that is used by nature, science and art, to which humans respond intuitively?

From the Pyramid of Cheops, height of the square root of **F** and height of its sides equal to **F**, measures already noted by Herodotus himself, proportions to the system devised by Le Corbusier, called *MODULOR*, based on the golden ratio and used in the construction of their modernist buildings, through the Parthenon or the statues of Michelangelo, architectural examples just to mention, and seem to bear.

**Fibonacci Sequence**

An interesting relationship between the call appears *Fibonacci Sequence* and the golden ratio.

*The Fibonacci* is formed by elements that are the sum of the above two, beginning with the number one: 1,2,3,5,8,13,21,34,55,89,144, Well ..., if we calculate the ratio between successive elements, see it,these ratios tend to the golden number φ.

Precisely this property underlies the construction of so-called *golden rectangle* you can draw squares fitting Fibonacci numbers so that progressively form turn golden rectangles. Construction to Mario Livio called "square boxes".

**Bibliography:**

Hemenway, P. The Secret Code.

Livio, Mario. The Golden Ratio.

Huntey, H.E. The Divine Proportion.

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