Nature always solves problems in the simplest and most elegant way you can think of. The golden ratio, or, in other words, the Fibonacci spiral, is a clear reflection of the genius of these solutions.
Traces of this proportion are found in ancient buildings and great paintings, the human body and celestial objects. For several centuries, the Golden Ratio and the Phi coefficient have been under the scrutiny of scientists from various fields.
Lucky Son
That's how, according to scientists, you can call Leonardo of Pisa, nicknamed Fibonacci. This nickname means that he is the son of Bonacci ("Bonacci" translates as "lucky"). A very funny fact, considering how many people he made happy indirectly, contributing to the development of mathematics, economics and other areas of knowledge, in which his discovery is now widely used.
This medieval Italian made such a great contribution to the development of modern science that it is very difficult to overestimate him. Dailyan increasing amount of scientific research is only confirming the principle, which he demonstrated to the world in the form of numbers.
Leonardo of Pisa is famous for presenting his sequential series of numbers, which constantly tends to the golden ratio.
Golden Ratio
This is a proportion that can be graphically represented as a segment divided by a dot into two parts. The most important rule of division: the entire segment is related to its larger part in the same way as the larger part is related to the smaller one.
That is, the point will divide the segment in such a way that if we divide the entire length (the sum of parts) by the value of the larger part, we get the same number as when dividing the larger part by the smaller one.
The result of division is always the same result - 1, 618. It is called the Phi coefficient.
Fibonacci numbers
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and beyond - these numbers have been playing a huge role in science for several centuries now.
They were called "Fibonacci series" or "Fibonacci numbers". The most important property of a sequence is that each new number is equal to the sum of the previous two. The so-called golden spiral of Fibonacci became a reflection of this particular sequence. It was she who brought him great fame.
But few people know that the contribution of the scientist did not end on the Fibonacci spiral alone. This medieval mathematician taught Europe to use Arabic in mathematics.figures, which greatly accelerated the development of science. Surprisingly, before he wrote a treatise on Arabic numerals, all of Europe used the Roman system exclusively.
Who knows how science would develop if not for his bright mind.
Phi coefficient
The most important number in the golden ratio is 1, 618. It is also present in the Fibonacci sequence. It is to this coefficient that the ratio of each next number to the previous one tends. That is why the discovery of the Fibonacci series has had such an impact on the entire scientific community. With the advent of mathematical exact expression, humanity has received a way to apply one of the most important laws of the surrounding world in new inventions and research.
This is the perfect number, the golden mean and a brilliant solution that nature itself uses everywhere.
Popular through the ages
The first mention of the principle of the golden ratio appeared in the time of Pythagoras. Since then, scientists have always observed this proportion, studied it and built all sorts of conjectures and assumptions.
In the modern world, this phenomenon has received wide publicity after the release of the film "The Da Vinci Code". In this picture, the filmmakers drew the attention of a wide audience to the fact that the golden ratio is used and found everywhere. It was mentioned there that proportion is observed everywhere, even in the human body. And naturally, a lot of people immediately became interested in this topic. Interest in the golden ratio, which arose thanks to this film, has not subsided so far. Internetfilled a huge number of "living" Fibonacci spirals in the photo: waves, cyclones, plants, mollusks … All these pictures over and over again show the beauty of one of the most important laws of nature.
How to draw a Fibonacci spiral
It is quite logical that having learned so much about this wonderful "curl", someone will probably want to create his own analogue.
It's easy enough to do. It is enough to have on hand a compass and a notebook in a box or graph paper (or a ruler that will help you build symmetrical, neat squares).
You need to start building the Fibonacci spiral from the image of two identical squares with a side length of one unit of length. The arc connecting the two opposite corners of the first square will become the beginning of the golden spiral. As the latter unwinds, an increasing number of proportional figures join it, until the desired size of the spiral is reached. The most important thing is to follow the rule where the length of the side of each next square is always equal to the sum of the lengths of the sides of the previous two.
Gold Rectangle
Ideal, from the point of view of the Fibonacci spiral, a rectangle has sides, the length of which is proportional to each other precisely by the phi coefficient. In other words, when dividing one side by the other, you must necessarily get 1.618 or 0.618 (the reciprocal of the phi coefficient).
Such rectangles are quite common inarchitecture and composition. It is also interesting what most people consider them to be "ideal" or "correct" from a visual point of view. In other words, a person intuitively perceives these proportions as more beautiful and natural, pleasing to the eye. Even when it comes to geometric shapes.
In art
If you mark the main elements in the paintings with dots or lines and divide the canvas into many small Fibonacci rectangles, you will notice an interesting fact. On a huge number of works of art, the figures are placed in such a way that obvious contrasts and important elements will certainly be on the edges of the rectangles or located directly on the Fibonacci spiral itself.
Moreover, self-respecting modern architects and designers are also true to this principle. And there is nothing surprising in this. The spiral reflects the law of nature itself, and she is a brilliant creator.
Some amazing and interesting facts
- More recently, there has even been a sort of social media craze for pictures of girls tossing their hair in the water, getting lots of beautiful splashes in the shape of a Fibonacci spiral.
- Many traders consider the principle very significant, based on the numbers of the Fibonacci series of strategies for selling and buying currencies.
- The ratio of the peaks of the cardiogram also falls under the golden ratio.
- In metallurgy, the fact has long been known that alloys of various metals have better resistance properties if the specificthe weight of the elements relates to each other according to the coefficient Phi.
- The proportions of various substances in hemoglobin are subject to this law.
- There is even an officially registered Golden Ratio Institute.
- In addition to the direct phi coefficient, there is also an inversely proportional number 0, 618, which is also often used in various calculations.
All fundamental knowledge mankind received by observing the world around. Over and over again, people have noted patterns in the change of seasons, found the relationship between thunder and lightning, studied the stars and created calendars.
The law of the golden section is just on the surface. And the Fibonacci spirals in nature, as a reflection of the principle to which all living things correspond, are found in a huge number of phenomena, in the plant and animal worlds.
This is exactly how, according to the principle of the golden section, living organisms develop most harmoniously. Each next step is only the sum of the previous two. Each next turn of the spiral grows gradually, opening up more and more, but repeating the general direction.
This is one of the greatest laws of the universe.
