Golden Ratio - a universal manifestation of structural harmony. It is found in nature, science, art - in all, what can a person get in touch. Once acquainted with the golden rule of humanity more than it did not change.
definition
The most comprehensive definition of the golden section states that the smaller part relates to more like a big - to the whole. Approximate its value - 1.6180339887. The rounded percentage value of the proportion of parts of the whole are related as 62% to 38%. This relation is valid forms of space and time.
The ancients saw in the golden section of the cosmic order reflection, and Johannes Kepler called it one of the treasures of geometry. Modern science considers the golden section as an "asymmetrical symmetry", calling it in a broad sense, a universal rule that reflects the structure and order of our world order.
History
The concept of the golden ratio were the ancient Egyptians knew about them, and in Russia, but for the first time science golden ratio explained monk Luca Pacioli book "Divine Proportion" (1509), illustrations of which allegedly made by Leonardo da Vinci. Pacioli saw in the golden section divine trinity: a small segment represented Son, large - the Father, and the whole - the Holy Spirit.
The direct way to the golden section rule connected with the name of the Italian mathematician Leonardo Fibonacci. As a result, the solution of one of the tasks of the scientist came to a sequence of numbers, now known as the Fibonacci series: 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. On the attitude of the sequence to the golden proportion noticed Kepler: "It is arranged so that the two least this never-ending proportions members add up to the third term, and any last two terms, if you combine them, give the next term, and the same proportion is stored indefinitely ". Now the Fibonacci series - is an arithmetic basis for calculating the proportions of the golden section in all its manifestations.
Leonardo also devoted much time to the study of the features of the golden section, most likely, it belongs to him, and the term itself. His drawings stereometric body formed by regular pentagons, prove that each of the rectangles obtained by cross-sectional aspect ratio gives the golden division.
Over time, the rule of the golden section turned into an academic routine, and only philosopher Adolf Zeising returned to him a second life in 1855. He brought to the absolute proportions of the golden section, making them universal for all the phenomena of the world. However, his "mathematical aestheticism" caused a lot of criticism.
Nature
Even without going into the calculations, the golden ratio can be easily found in nature. So, get under it the ratio of the tail and body of lizard, the distance between the leaves on a branch, there is the golden section in the shape of an egg, if the conventional line to push through its widest part.
Belarusian scientist Eduard Soroko, who has studied the form of gold division in nature, pointed out that all growing and striving to take its place in space, endowed with the proportions of the golden section. In his opinion, one of the most interesting forms of this cockling.
Even Archimedes, focusing spiral brought on the basis of its form equation which now is used in the art. Later, Goethe noted the attraction of nature to the spiral shape, spiral calling "life curve". Modern scientists have found that such manifestations of spiral forms in nature as a snail shell, the arrangement of sunflower seeds, web designs, storm motion, the structure of DNA, and even the structure of galaxies comprise the Fibonacci series.
Human
Designers and fashion designers are doing all the calculations based on the proportions of the golden section. Man - this is a universal form to check the laws of the golden section. Of course, by nature not all people are perfect proportions, which creates certain difficulties with the selection of clothing.
In the diary of Leonardo da Vinci a drawing inscribed in a circle of a naked person in two positions superposed. Based on the study of the Roman architect Vitruvius, Leonardo tried to establish a similar way the human body proportions. Later, the French architect Le Corbusier, using the "Vitruvian Man" by Leonardo, has created his own scale of "harmonic proportions", affect the aesthetics of the XX century architecture.
Adolf Zeising by examining the proportionality of the man has done a great job. It measured about two thousand human bodies, as well as many ancient statues and deduced that the golden ratio expresses the average law. The man he subordinated almost all parts of the body, but the main indicator of the golden section is a division of the body point of the navel.
The measurements the researchers found that male body proportions 13: 8 closer to the golden ratio, what proportion of the female body - 8: 5.
The art of spatial forms
Artist Vasily Surikov said, "that there is an immutable law of composition when the film can not remove anything either, nor to add even extra point can not be delivered, it is a real mathematician." For a long time the artists have followed this law intuitively, but after Leonardo da Vinci, the process of creating beautiful paintings is not complete without solving geometric problems. For example, Albrecht Dürer to determine the points of the golden section used the invention of proportional compasses.
Art F. Kovalev, studied in detail the picture of Nikolai Ge "Alexander Pushkin in the village of St. Michael", notes that every detail of the web, whether a fireplace, a bookcase, a chair or a poet himself, strictly written in the golden ratio.
Researchers golden section tireless study and measure the masterpieces of architecture, arguing that they have become established, because the established canons for gold: on their list of The Great Pyramids of Giza, Notre Dame, St. Basil's Cathedral, the Parthenon.
And today, in any art of spatial forms are trying to follow the proportions of the golden section, as they are, according to critics, the perception of the product and make it easier to form the viewer a sense of aesthetic.
The word, sound and filmstrip
Form temporarily? Of art in its own way, we demonstrate the principle of the golden division. Literary critics, for example, noticed that the most popular number of lines in the poems of the late period of Pushkin's work corresponds to the Fibonacci series - 5, 8, 13, 21, 34.
The rule of the golden section and in individual works of Russian classics. As the culmination of "The Queen of Spades" is a dramatic scene Herman and Countess, ending with the death of the latter. The story line 853, and the climax falls on line 535 (853: 535 = 1.6) - this is the point of the golden section.
Soviet musicologist E. K. Rosen notes the striking accuracy of the golden section ratio in the strict and free forms of the works of Johann Sebastian Bach, which corresponds to a thoughtful, focused, technically well thought-out style of the master. This is true of the outstanding works of other composers, where the golden section point usually have the most vivid and unexpected music solution.
Film director Sergei Eisenstein script of his film "Battleship Potemkin" deliberately coordinated with the rule of the golden section, dividing the tape into five parts. In the first three sections of the action takes place on the ship, and the last two - in Odessa. The transition to the stage in the city and there is a happy medium film.
