The shape of the subject, which is based on the ratio of the golden ratio, as psychologists and mathematicians have proved, is perceived by man as beauty and harmony. The golden ratio in mathematics is such a division into parts of a segment, when the entire segment refers to the greater part, as the larger refers to the smaller part.
It is believed that the concept of the golden ratio was first introduced by Pythagoras. There is an assumption that he took his knowledge of what the golden ratio is in mathematics and not only in it, but also in architecture, painting, art and much more, from the Babylonians and Egyptians. In fact, the proportions of temples, the pyramids of Cheops, and some household items indicate that craftsmen from Egypt used the ratio of the golden ratio in their construction and manufacture.
Plato was also aware of the golden ratio. In his “Timaeus” dialogue, he considers issues related to the aesthetic and mathematical aspects of the Pythagorean school, including the problems of the golden ratio.
In the proportions of the facade of the Parthenon temple, the presence of a gold division is noted. When excavating this temple, compasses were found that were used by sculptors and architects of ancient Greece. The compass found in Pompeii, which is now in the museum in Naples, also contains these divine proportions.
The first mention of the golden division in ancient literature that has come down to us can be found in the "Beginnings" of Euclid, where the construction of the golden section is given geometrically.
In medieval Europe, the secrets of the golden section were kept in strict secrecy, carefully guarded. They could only be known to the initiates.
During the Renaissance, interest in gold division intensifies. The brilliant artist and scientist Leonardo da Vinci, of course, could not know about the divine proportion and used it in his works. In addition, he began to write a book on geometry, where he wanted to show the wonders of the golden ratio, but he was ahead of the monk and great mathematician of Italy Luca Pacioli, who published the book "Divine Proportion" in Venice in 1509.
Middle Ages mathematician Leonardo of Pisa (born c. 1170 - d. C. 1250), better known as Fibonacci, was one of the famous scientists of that time. For the first time in Europe, he used Arabic instead of Roman numerals and discovered a sequence of numbers in mathematics, later named after Fibonacci. It looks like this: 1,1,2,3,5,8,13,21, ... and so on. The sequence of such numbers is called sometimes Fibonacci numbers. The golden ratio is visible here. You may notice that in this sequence of numbers each following is formed if the two previous ones are added. If we divide each subsequent member of this remarkable sequence into the previous one, we will get a gradual approximation to the Fibonacci number ( = 1,6180339 ...). This is the Fibonacci golden ratio, expressed by the number F. This number, like the famous number Pi = 3.1415 ..., does not have an exact value. After the decimal point, the number of digits is infinite. This is how the golden ratio manifests itself in mathematics. So mathematical and not only miracles begin. If we divide any member of the sequence into the next one, we get the number 0, 6180339 ... Miracles happen again - after the decimal point, the digits repeat exactly all the digits of the number , only the decimal point is not 1, but 0. There are a lot of similar mathematical paradoxes . And this is just the beginning. The golden ratio in mathematics and not only in it simply works wonders, only we sometimes do not notice it.
It exists in architecture, and in music, in mathematics, poetry, economics, in the structure of plants, in the stock market, in the proportions of the human body and animal bodies, in the spiral of a snail, in the macro and microworld, in the Universe and so on, until infinity ...
So, we can make an assumption that the Golden Ratio (Golden proportion, Divine proportion) is present at all levels of the universe.