Ah, Tuscany! In this cradle of the Renaissance and Italian culture we literally walk in the footsteps of giants. Michelangelo, Leonardo, Galileo and many others. This is the crossroads for research on beauty and numbers. Although already included by the Pythagoreans, it is there, in the renaissance, that this relationship was finally documented. In particular by the mathematician Luca Pacioli in his book "Divine proportion". The book was illustrated by Leonardo da Vinci himself. The work of the genius is a witness to his search for the perfect proportion. This research played a large role for the artists of the Renaissance. In architecture, sculpture, painting and even music they studied and developed the knowledge of the ancients.
Numbers from the Orient
After centuries of darkness, the light of the Greek and Oriental Sciences finally penetrated Europe. Tuscany was a commercial crossroads between East and West. Two centuries before the Renaissance, a representative of the merchants of the Republic of Pisa in Algeria named Bonacci, sent his son to study mathematics. This son of Bonacci (Fibonacci) introduced in Italy the algorism (deformation of Al Khawrzimi and origin of the word algorithm). Long before dealing with computers this word defined a preacher of what Khawarizmi preached to the Arabs, the decimal system born in India and now called Arabic numerals.
Fibonacci sequence and the golden ratio, Phi
Fibonacci certainly did not suspect that his name will become famous in relation to a sordid thing, a sequence for predicting breeding rabbits. In his sequence, a number is the sum of the previous two.
1 + 1 = 2, 2 + 1 = 3, 3 + 2 = 5, 5 + 3 = 8, 5 + 8 = 13, 8 + 13 = 21, ... 34, ... 55, ... 89 ... ... 144
Today we know that this sequence is directly related to the "divine proportion". Although no ratio can rule on the golden ratio, irrational among the irrationals, the ratio of two successive Fibonacci numbers draw closer to the golden ratio as it grows.