Thursday, 2 May 2013

The divine proportion

"Let me interpret those who are not mathematicians," is often cited thought to be attributed to Leonardo da Vinci (1452-1519), one of the greatest artists, scientists and researchers that human civilization had.
And today, while Leonardo's works continue to provoke a lot of attention and nothing less deflection due to the mystique that they are easily attributed to, we can not but admit that the sight of them gives the impression of absolute harmony and infinity, something that in real life there does not exist.
That impression and feeling that makes short work of finishing work and thousands of sketches, drawings and illustrations testify to the part of a man who is making the time when the Middle Ages off and abandoned, ancient love for a man woke, he tried to trace the remains of the past and find eternal , immutable truth, universal in every society and in every person.
Leonardo's work carries a testimony to the spirit of the Renaissance, when humanism as the philosophical ideas of the epoch and cope with the challenges and temptations of superstition and ignorance.
Leonardo's paintings, famous not only in the original, but the ubiquitous reproductions - Adoration of the Magi (1481), The Last Supper (1498), Mona Lisa (c. 1505), SS. John the Baptist (1514) - the most important part of the world's artistic heritage.
There is, however, a piece that its structure and content provides an excellent introduction to the story of the relationship of the great artist and mathematics. This is a drawing of a man Vitruvijanski (around 1485), the male figure, which seems to float in an undefined space limited only by thin lines, squares and circles.
Referring to Vitruvius, a Roman architect celebrated the end of the old era, Leonardo consciously reveal who his role models and where the search for answers to their questions more numerous.
If we follow his writings, known as codices, which he, texts and drawings, almost frantically, constantly and daily meet, we all topics and areas covered by this humanist and certainly the biggest homo universalis the world has seen.
At more than 5,000 pages of Leonardo's records are thinking, analysis and findings in such diverse scientific disciplines such as aeronautics and anatomy, botany and mechanics, cartography and hydraulics, acoustics and weapons production, urbanism and optics.

This, in fact, as if it required a clear classification, our in measure and number, by Leonardo gets a random (?) Encounter with Luke Pacolli (1446-1516) in Milan, during the painting of the Last Supper for the Church of Santa Maria della Grazie, probably 1496/97. year.
Since then, the next ten years, Leonardo Paco are inseparable friends, associates and researchers, who are trying to revive and restore long-forgotten ancient knowledge. Pacoima, a Franciscan monk, and Leonard became a mathematics teacher who helps him to acquire mathematical knowledge necessary for further development of his ideas and work.
Their collaboration culminated in the publication of three manuscript versions Pačolijevog file Proportione Divina - the divine proportion, in the late 15th century, in which Pacoima successively for the next few years.
To book his friend Leonardo prepares drawings illustrating the golden ratio, proportion, and models of polyhedra highlighted by the many ancient philosophers and mathematicians such as Plato, Euclid and Archimedes.
The Renaissance man polyhedra admired as an extraordinary body of beauty. Dodecahedron are thus seen as a representation of the universe in all its glory and integrity. In addition polyhedra Leonardo designs and letters of the alphabet - the initials of which is perhaps the most famous big "M" that the Metropolitan Museum of New York uses as its logo.
As the first printed edition of this work was not published until 1509, several years after scattering Leonard and Pacolli belated glory of theoretical mathematics from the file begins to spread among and between artists and scientists.
In the early 16th century, the divine proportion becomes as indispensable reading for all those concerned with mathematics, but they need Leonardo visuals. At that time, Pacoima to Venice writes that "in Milan polyhedra made sublime painter, architect, musician, and a universal genius, Florentine Leonardo da Vinci."

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