GROUP: Matteo Visentin (Treviso, Italy); Chesar Nicoleta Ruxandra, Hutanu Alexandra, Marinela, Matinca Loredana Daniela, Elena (Bucuresti, Romania);Apostolos Kampas, Filitsa Kougioumtzoglou, Lefteris Katsoulas, Antonis Katsoulas, Panagiotis Digidikis, Polina Koutsovili, Ralitsa Mitova Goreja Maria (Mytilene, Greece)

###### THE GOLDEN RATIO

The golden ratio is a number used mainly in maths and architecture, it applied to indicate the ration between two irregular

length and it is usually associated to the symbol (phi).

We can see if we dived a line in two parts the longer part ( ) dived by the smaller is equivalent to the

line itself dived by the longer part of it.

This ratio can be expressed by the rule

Applying that form (ideated by *Euclid*) we obtain the value of the golden number which is about **1,6180**

Another way to calculate the value of it is building the golden rectangle which is equivalent to:

Let's see how:

So now we are able to derive by that figure the ratio:

Ending with a simple calculation: =

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**GEOMETRY**

In geometry we can often find the golden ratio especially in shapes like dodecahedron, pentagram, pentagon and decagon as the

ancient Greeks already discovered but there are a couple ok golden polygons in which we can recognize the golden ration, the

most characteristic is the golden rectangle followed by the golden triangle in which the ration is between the equal sides and the base.

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**ART**

In Da Vinci's work **'Mona Lisa'** we can note that the face of the woman is a perfect golden rectangle, moreover the golden ratio is

evident in the areas from the base of the neck to the center of the pupil, from the base of the neck to the top of the forehead, from

the right side of the face to the right side of the top of the nose and from the bottom of the chin to the part above the hands

In *Greek sculture* the golden ratio has been widely used, for example in the **Status of Athena**,we can recognize the first Golden Ratio in the

length from the front head to the ear opening compared with the length from the forehead to the chin

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**ARCHITECTURE**

It was used it in the design of Notre Dame in Paris, which was built in the 1163 and 1250.

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**EVERYDAY LIFE**

Also a *DNA molecule* is based on the Golden section. It measures 34 angstroms long and 21 angstroms wide for each full cycle of its double helix spiral.

The ratio between 34 and 21, is, 1.6190476 which is close to the value of Phi, 1.6180339.

Matteo Visentin