What do they have in common?


he lesser is to the greater as the greater is to the addition of both

A philosophical-looking premise which can be graphed as a rectangle where the shorter side divided by the longer one equals the latter divided by the addition of both. This, put in math terms and assuming the shorter side has a value equivalent to 1, is:

The solution to this equation is g=1.618... and infinite decimals; we will shorten it to 1.618). The name of this enigmatic number, known since ancient times, is Phi (not to be confused with Pi, whose value is 3.14159).

This means that the longer side is 1.618 times longer than the shorter one. Do you find this rectangle looks familiar? Of course. Banks know what they do.
It is the shape of your credit card!

Phi comes from Phidias, famous ancient sculptor, and this value is highly appreciated by painters, sculptors, architects and artists, who love employing it in their creations: Le Corbusier in the New York UN building, Picasso in its famous paint Gernika (in an elaborated way) and many many other at all times.

It is nevertheless most arguable that from the aesthetic point of view a 1.618:1 rectangle produces more pleasant and harmonic sensations than other noteworthy figures such as 1.359 (e/2):1, 1.4142 (sq root of 2; this is the ratio in popular DIN A4 sheets):1, 1.5 (3/2):1, 1.571 (Pi/2):1, 1.7321 (sq root of 3):1 or any vulgar number alike whatsoever. The 1.618:1 ratio is no doubt employed only as an homage to classic culture.

In a five-arm star inscribed into a regular pentagon, Phi appears out of dividing the length of different coloured segments in the star on the right.

Why this happens? Nobody knows.

The five-arm star, aka Pentalpha, is everywhere: in a lot of national flags, in Hollywood Walk of Fame, commercial logos, combat airplanes and vehicles, and even there are animals with that shape. In an ample sense, this star stands for the human being. For instance, a five-arm star rests obviously in Michelangelo's paint The Sacred Family (left) and in the US Pentagon (right).

Il signore Fibonacci, brilliant mathematician
He learnt the indo-arabic numeric system through commercial trips in North Africa. Even though this system has enormous advantages upon the Roman numeric one which was employed all over Europe at that time (AD 1300), the shift took many decades to be generally accepted. Fibonacci is well known by his sequence of numbers, where, starting with 1, an item is the sum of the two previous ones:

1    1    2    3    5    8    13    21    34    55   
89    144    233    etc

Values of these sequence are frequently found on living creatures, animals and plants. For instance, the value 5 (a body fitted with one head and four members) has succeeded in all kind of animals, including birds and the human being itself. Besides, if we divide two consecutive numbers of this series (the higher, the more accuracy) we will obtain... the enigmatic Phi!! For example:

More amazing facts: the square of Phi (2.61803398874...) has exactly the same decimals than the original one. And one divided by Phi... has the same decimals again!

All these things are really interesting,
but maybe the most fascinating fact is that


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