## Where does the Golden ratio come from ?

### The Golden ratio in Antiquity

Building has always been man's great ambition and the discovery of the Golden Number probably dates back to ancient times.

The Golden Number, in fact, is found more than 20 times in the 5-pointed star, and the division by 5 could be suggested by the great variety of flowers with 5 petals, the five branches of a starfish, the pentagonal structure of the sea urchin and its 5 teeth... Note, also, that man has 5 fingers on each limb and 5 senses which are all **pentagonal representations.**

**The number 5 gives rise to a relationship with Phi.**

If the monuments prior to the Hellenic civilization, in particular those of ancient Egypt (the pyramid of Cheops is 47 centuries old) reveal the empirical use of the Golden Number, the written texts dealing with its properties or rather with the **geometrical figures** which are linked to it will appear only with the Greeks.

Euclid, Pythagoras and many others gave the notion of the Golden Number mathematical rigor.

Three centuries before our era, Euclid with his "Elements", brings in this field an important contribution in the form of a geometrical demonstration: construction of an isosceles triangle having each of the angles at the base double of the remaining angle (i.e., in this famous isosceles triangle each of the angles at the base is worth 72 degrees and the angle of the top is equal to 36 degrees)

Note, also, that 72 degrees is the fifth of 360 degrees and 36 degrees the 10th of 360 degrees: angles that we find in the regular pentagon.

Euclid deduced from this triangle the construction of the regular pentagon, noting that the diagonals of this pentagon intersect in the middle and extreme right and that the ratio of the diagonal to the side is equal to Phi.

He ends his "Elements" with the inscription in a sphere of the five Platonic regular bodies: tetrahedron, octahedron, hexahedron (cube), icosahedron and dodecahedron.

Meditating on the Golden Section, Vitruvius came to the following conclusion: "*As the members of the body correspond to each other, so must the parts of the building*".

### The Golden ratio in the Middle Ages

In the 11th and 12th centuries, a time when faith was written in stone, 80 cathedrals were built in France, 500 large churches in monasteries and important towns and tens of thousands of parish churches. This is the era of Romanesque art: **geometric shapes**, sound and light vibrations are combined to reproduce the model of the universe that celebrates the greatness of the creator.

At the end of the Romanesque period, the search for the sky and the light is increasing; the cathedrals, at first squat, develop higher and higher vaults, giving birth to the gothic art.

Gothic art was born in France in the middle of the 12th century (the first Gothic vault was built in 1944 in the cathedral of Saint-Denis). This gothic art is characterized essentially by the use of vaults on ribbed crossings, of the broken arch instead of the round arch and of the buttress to support the main vault

The cathedral is a book of stone that exalts faith, harmony and beauty.

### The Golden ratio in the Renaissance

In the 15th century, it is known that the "Elements" of Euclid were taken up by Luca Pacioli, a Franciscan monk and professor of sacred theology, who knew perfectly well, through Euclid and Pythagoras, the division of a segment of a straight line into the mean and the extreme reason.

His book deals with architecture, the proportions of the human body and the letters of the alphabet

It is at the time of Pacioli, that is to say during the Renaissance, that the great artists, like his friend Leonardo da Vinci, adopted the Divine Proportion as a **canon of Beauty, of Harmony**. We will deal with this subject a little further on.