The most capacious definition of the golden ratio states that the lesser part refers to the greater part as the greater part refers to the whole. Its approximate value is 1.6180339887. In rounded percentages, the proportions of the parts of the whole would relate as 62% to 38%. This ratio is valid in the forms of space and time.
The ancients saw the golden ratio as a reflection of cosmic order, and Johannes Kepler called it one of the treasures of geometry. Modern science sees the golden ratio as "asymmetric symmetry", calling it in a broad sense a universal rule reflecting the structure and order of our world order.
The ancient Egyptians had an idea about golden ratio, the Russians also knew about them, but the first scientific explanation of the golden ratio was given by a monk Luca Pacioli in the book "The divine proportion" (1509), the illustrations to which supposedly made Leonardo da Vinci. Pacioli saw the golden ratio as a divine trinity: the smallest section represented the Son, the largest section the Father, and the whole the Holy Spirit.
Directly related to the golden ratio rule is the name of Italian mathematician Leonardo Fibonacci. As a result of solving one of his problems, the scientist found a sequence of numbers, now known as the Fibonacci numbers: 0, 1, 1, 2, 3... etc. Kepler noticed the attitude of this sequence to the golden proportion: "It is made in such a way that two least members of this infinite proportion, added together, give a third term, and any two last members, if added together, give the next one, and the same proportion is kept till infinity". Now the Fibonacci series is the arithmetic basis for calculating the proportions of the golden ratio in all its manifestations.
Leonardo da Vinci also spent a lot of time studying the features of the golden ratio, most likely he owns the term itself. His drawings of a stereometric body formed by regular pentagons prove that each of the rectangles obtained in the section gives the ratio of the sides in the golden ratio.
Over time, the rule of the golden ratio turned into an academic routine, and only the philosopher Adolf Zeising gave it a second life back in 1855. He brought the proportions of the golden ratio to the absolute, making them universal for all phenomena of the world. His "mathematical aesthetics," however, provoked much criticism.
The nature of
Even without going into the calculations, the golden ratio can easily be found in nature. For example, it fits the ratio of the tail and body of a lizard, the distance between the leaves on a branch, there is a golden ratio in the shape of an egg, if the conventional line is drawn through its widest part.
Belarusian scientist Eduard Soroko, who studied the forms of golden divisions in nature, noted that everything that grows and strives to take its place in space is endowed with the proportions of the golden ratio. In his opinion, one of the most interesting forms is the spiral curl.
Even Archimedes, paying attention to the spiral, derived an equation based on its shape, which is still used in engineering. Goethe later noted nature's attraction to spiral forms, calling the spiral "the curve of life." Modern scientists have found that such manifestations of spiral forms in nature as the snail shell, the arrangement of sunflower seeds, the patterns of spider webs, the movement of a hurricane, the structure of DNA and even the structure of galaxies comprise the Fibonacci series.
Fashion designers and designers of clothing make all calculations based on the proportions of the golden ratio. Man is a universal form for testing the laws of the golden ratio. Of course, by nature, not all people have ideal proportions, which creates certain difficulties with the selection of clothes.