## What does the "golden section" mean?

Oddly enough, but to give a simple definition of the golden section is quite difficult. Most understandable, it sounds like this: the golden proportion is manifested when a smaller part of the whole belongs to the greater part just as much as a larger part to the whole. If this ratio is expressed in terms of numbers, then the integer is 1, most of which will be about 0.62, and less than about 0.38.

## How to investigate the "golden section"? A bit of history

There is no doubt that ancient civilizations knew about the golden proportion. This is evidenced by the principles of the construction of the Egyptian and Mesoamerican pyramids. Also, according to the principle of the golden section, sacred places in ancient Greece were connected.

History suggests that the first to introduce the concept of the golden section to science was Pythagoras in the 6th century. BC O., and the necessary information he received from the ancient Egyptian and Babylonian sources. It is believed that the study of the golden section was the main task in the famous school of the Pythagoreans.

Later, in the III. BC e., was first described the geometric construction of the golden proportion. In any case, the sources that have reached us testify to this. The great mathematician Euclid portrayed him on his “Golden Pentagon” in the main work of his life, “The Beginning”. One of the features of the pentagon is that the ratio of adjacent angles when it is built is 0.4 to 0.6, that is, close to the "golden" angle. After Euclid's research continued Gipiskl (II century. BC. E.) And Papp (III century. BC. E.).

In the Middle Ages and the Renaissance, many scientists, architects, sculptors and artists actively study and apply the golden proportion. The most famous of them is Leonardo da Vinci. Many authoritative sources say that he is the author of the term "golden section". In his paintings, every detail takes its specific place. The position and dimensions of parts are interconnected in a ratio of 0.62 to 0.38. Thanks to this, the works were done ingeniously skillfully and look very harmonious. And such paintings as “Gioconda” or “Vitruvian Man” are probably the best examples of how to use the golden section in art.

One of the greatest works on the golden proportion was also written in the Renaissance. In 1509, the great Italian mathematician Fra Luca Pacioli published his treatise On Divine Proportion, which revealed the principles of the "golden section" and was a real tool for artists, mathematicians and architects. He finished the book of Pacioli in his old age, 8 years before his death. The conclusion is that a person has devoted his life to the study of one important issue. It is worth noting that the treatise was beautifully illustrated, since it was written jointly with Leonardo da Vinci.

After the Renaissance, interest in the study of the golden section declined until the 20th century. In the XX century. creative people and mathematicians again began to study the forgotten topic. At this time, there is a new famous explorer of a unique phenomenon - the French architect Le Corbusier. In his book "Modulor", Le Corbusier proposes to use in the architecture a system of quantities interconnected by the golden proportion. As the main value, he took the average height of a person (it was assumed that it is 175 cm). In his opinion, the system allowed to make buildings the most harmonious and functional.

One of the first to rate Le Corbusier’s system was Albert Einstein. After reviewing the "Modular", he wrote to the architect with the following words: **"This is a range of proportions that makes bad difficult and good easily attainable."**

Despite this, the works of Le Corbusier were regularly criticized, they were called unfounded and improperly designed. For example, a lot of controversy arose over the average human growth. Critics believed that 175 cm - arbitrarily taken value. At the same time, we still note that his architectural projects are quite functional, and they are used in construction to this day.

## How to apply the "golden proportion" in life?

From the above, we can conclude that the more connections (be it a company, a country's economy, a school, or a human body) correspond to the ratio of 0.38 to 0.62, the more stable and harmonious this system will be.

In every object, in every case, in every system there are components that can be linked to each other with the help of the golden proportion. Thus, the components and the whole will be in balance.

Here are some examples of how to apply the golden proportion in your life.

In accordance with the proportion can build a learning process. For example, devote 62% of the time to practice, and 38% - the theory. In this case, the person will get a good experience and gain enough general knowledge. Or you can devote most of your time to theory to be a broader specialist and have enough experience.

In the same way you can distribute the super profits of the company. 62% of super profits to invest, and the remaining 38% used as a bonus to staff.

As an example, we can cite a firm that, according to the "golden proportion", set the wages of workers. The salary of a lower-skilled worker was 62% of the next level worker’s salary, and his salary was 62% of the next above him. Thanks to this innovation, wages were not too high, and the workers were motivated to increase their level of knowledge in order to earn more.

Even your own free time can be divided into parts according to the principle of free section. If you go for a walk, try about 62% of the time to walk and see the sights or nature, and 38% of the time to spend in a cafe, bar or on a halt. Thus, you will scatter, learn something new and do not get too tired of the long road.

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