Form object, which is based on the ratio of the golden ratio as proven by psychologists and mathematicians, is perceived by man as beauty and harmony.The golden section in mathematics - it is the division into parts of the segment when the whole segment applies to most of the way most of the lesser parts.
believed that the concept of the golden section was first introduced by Pythagoras.There is speculation that he is your knowledge of what is the golden section in mathematics and not only there, but also in architecture, painting, art and much more, I took the Babylonians and Egyptians.In fact, the proportion of temples, pyramids of Cheops, some household items indicate that the masters of Egypt used the ratio of the golden ratio in their construction and manufacture.
Plato, too, was aware of the golden section.In his dialogue "Timaeus", he addresses issues related to aesthetic and mathematical aspects of the Pythagorean school, including the problems of the golden ratio.
The proportions of the facade of the Parthenon temple is noted the presence of the gold division.During the excavation of the temple were found compasses, who used architects and sculptors of ancient Greece.The results in Pompeii compass, which is now in the museum in Naples, also laid the divine proportion.
first mention of the gold division in ancient literature, extant, can be found in the "Elements" of Euclid, which provides construction of the Golden Section geometrically.
In medieval Europe the secrets of the golden section were kept in strict secrecy, carefully preserved.They could be known only to the initiated.
During the Renaissance interest in the gold division increases.The brilliant artist and scientist Leonardo da Vinci, of course, could not know the divine proportion and used it in their works.In addition, he began to write a book on geometry, where he wanted to show the wonders of the golden ratio, but it was ahead of the monk and the great mathematician Luca Pacioli in Italy, which in Venice in 1509 published the book "The Divine Proportion."
medieval mathematician Leonardo of Pisa (b. C. 1170 - d. C. 1250), better known as Fibonacci, it was one of the famous scientists of the time.For the first time in Europe, he used the Roman numerals instead of Arabic and discovered a series 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 numbers is called sometimes Fibonacci numbers.The golden section can be seen here.You can see that in this sequence of numbers, each in the following way, if you add the two preceding.If we divide each term of the remarkable sequence of the previous one, we get a gradual approach to the Fibonacci number (P = 1.6180339 ...).This is the Fibonacci golden ratio, expressed as the number of F. This number, as well as the famous pi = 3.1415 ..., does not have an exact value.After a point is infinite number of digits.So manifests the golden section in mathematics.Thus begins the math and not just miracles.If we divide each term of the sequence to the next, we get the number 0, 6180339 ... Miracles happen again - digits after the decimal point is repeated exactly all the numbers of F, just before the comma is not 1 and 0. Such mathematical paradoxes here very much.And that's just the beginning.The golden section in mathematics and not only it works wonders, but we sometimes do not notice.
It is both in architecture and in music, mathematics, poetry, the economy, the structure of plants in the stock market, in the proportions of the human body and the bodies of animals, spiral snail in macro and microcosm, the universe and so onad infinitum ...
So, we can assume that Golden Ratio (Golden Proportion, Divine Proportion) is present at all levels of the universe.
