It is a sequence of numbers that appears encoded in many natural phenomena. Described at the end of the 12th century by the Italian mathematician Leonardo Fibonacci, it is infinite and starts with 0 and 1. The following numbers are always the sum of the two previous numbers. Therefore: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34…
The terms in the sequence establish the so-called golden ratio (or ratio) among themselves, widely used in art, architecture and design because it is considered pleasing to the eye. Its value is 1.618… It is an irrational, infinite number, represented in mathematics by the Greek letter phi: φ.
The further you go in the Fibonacci sequence, the more the division between a term and its predecessor approaches this number. Check it out:
two ÷ 1 = 2
3 ÷ 2 = 1.5
5 ÷ 3 = 1.666…
8 ÷ 5 = 1.6
13 ÷ 8 = 1.625
21 ÷ 13 = 1.615
The famous Fibonacci Spiral drawing, which you see below, works like this: take the two largest squares in the illustration. If the larger left square is 1.618 cm on a side, then the smaller right square is 1 cm. Thus, dividing the size of one by the other gives the golden ratio: 1.618… ÷ 1 = 1.618…
The fun thing is that any pair of squares you select will follow the same proportion to each other, so the design is an eternal repetition of itself in smaller and smaller versions.
The spiral and the Fibonacci sequence are one easter egg from nature. Check out some of his illustrious appearances:
Concha do snail: each new piece has the dimension of the sum of the two predecessors;
Chameleon: contracted, its tail is one of the most perfect representations of the Fibonacci spiral;
Elephant: if your ivory tusks grew non-stop, at the end of the process, guess what shape it would be?
Sunflower: its seeds fill the core arranged in two sets of spirals: generally, 21 clockwise and 34 counterclockwise;
Cone: the seeds grow and are organized in two spirals that resemble Fibonacci: eight radiating clockwise and 13 counterclockwise;
Poetry: the “golden number” even appears in the ratio between the major and minor stanzas of the Iliad, Homer’s epic about the last days of the Trojan War;
Parthenon: the Greeks already knew the proportion, although not the formula to define it. The width and height of the facade of this fifth-century BC temple are in the ratio of 1 to 1.618;
Egyptian Pyramids: Each block is 1,618 times larger than the block in the next level above. In some, the inner chambers are 1,618 times longer than their width;
Layout: several credit card formats have already been tested. What became public favorites have sides in the golden ratio. Pictures in newspapers also tend to adopt it.
Sources: Roberto Jamal, professor at the Anglo course, Claudio Possani, professor at the Institute of Mathematics and Statistics at USP.