With the manifestation of such an effect as the "golden ratio", it seems, almost every person encountered in childhood. If we, guided by this principle, cut a smaller rectangle from a rectangular sheet of paper, then we will definitely get a figure with exactly the same aspect ratio. This, in fact, is the simplest content of the principle of the golden section. A more scientific definition is as follows: the golden ratio is the operation of dividing a certain continuous value into 2 parts in such a proportion that the smaller part refers to the larger one, as the larger one refers to the entire value.
The history of this pattern is quite large. Even in antiquity, the mention of it was first encountered by Euclid in his famous work “Beginnings”. Euclid uses this rule to build some geometric shapes. Pattern was so common that in the days of Leonardo da Vinci it was called "divine proportion", and the term itself was introduced into use by Martin Om in 1835.
Indeed, the prevalence of this phenomenon is simply amazing, some people generally seek to "see" the signs of the golden section in the whole world around them, and even in everyday events. There was even an ironic joke about this, which says that many people find it possible to detect the presence of signs of the golden ratio everywhere and in everything.
Vividly reproduce the effect of geometric proportions. The golden ratio, for example, used in a regular five-pointed star, manifests itself in that, each segment connecting the rays of the star with each other is divided by another segment intersecting it, according to the rule of this proportion.
The golden ratio is widely represented in works of art and sculpture, common in architecture. In these areas of activity, it is usually understood as an asymmetric construction or composition that contains the proportions of the section. Moreover, it is not always possible to express the essence of this entire construction mathematically.
There is an opinion that objects and objects, which include elements containing a golden section, are perceived as the most harmonious and attractive. But this is not always the case, because it may be just a coincidence or a mistake in perception. For example, it is generally accepted that the proportions of the famous pyramid indicate that the Egyptians used these ratios. Some even find signs of sectional proportions in music. For example, some scholars argue that these principles are entirely based on musical works of the Baroque era , including the works of the great Beethoven, Bach and Mozart.
There are many examples that demonstrate evidence of the pros and cons of the presence of signs of the golden ratio in a particular area of human activity. However, it should be recognized unequivocal that the golden section in nature is widespread enough, it only needs to be "seen".
The astronomer Johannes Kepler called this proportion a treasure of geometry, and saw its manifestation in botany - on the example of the structure and growth of plants that preserve the specified proportions during growth. German researcher Zeising measured 2,000 human bodies and established the pattern of dividing the body by the navel in a proportion corresponding to the golden ratio. The proportions familiar to the eye can be seen in the lizard - the tail and the rest of the body are correlated in length in the ratio of 62 to 38. As you can see, in the plant and animal world, a tendency toward shaping, which contains signs of a golden proportion, is quite clearly seen.
Nature, as it were, produces division according to the rules of symmetry and the golden ratio.