Nature always solves problems in the simplest and most elegant way that you can think of. The golden ratio, or, in other words, the Fibonacci spiral, is a clear reflection of the genius of these decisions.
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 Phi ratio have been under the scrutiny of scientists from various fields.
"Lucky son"
That is, according to scientists, can be called Leonardo of Pisa, nicknamed Fibonacci. This nickname means that he is the son of Bonachchi ("Bonachi" is translated as "lucky"). A very funny fact, given 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. Every day, an increasing number of scientific studies only confirms the principle, which he clearly showed the whole world in the form of numbers.
Leonardo of Pisa is famous for presenting his consecutive series of numbers, which is constantly striving for the golden ratio.
Golden ratio
This is the proportion that can be graphically depicted as a segment divided by a point into two parts. The most important rule of division: the whole segment refers to its greater part in the same way as the majority refers 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 the parts) by the size of the larger part, we will get the same number as when dividing the larger part by the smaller one.
As a result of division, the same result is always obtained - 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 figures have been playing a huge role in science for several centuries.
They were called the Fibonacci series or the Fibonacci numbers. The most important property of the sequence is that each new number is equal to the sum of the previous two. The reflection of this particular sequence has become the so-called golden Fibonacci spiral. It was she who brought him great fame.
But few people know that on the Fibonacci spiral alone, the contribution of the scientist did not end. This medieval mathematician taught Europe to use Arabic numerals in mathematics, which greatly accelerated the development of science. Surprisingly, until he wrote a treatise on Arabic numerals, all of Europe used the Roman system exclusively.
Who knows how science would have developed if not for his bright mind.
The coefficient "Phi"
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 strives. That is why the discovery of the Fibonacci series has so affected 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 world in new inventions and studies.
This is a perfect number, a middle ground and a brilliant solution that nature itself uses everywhere.
Popularity 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 various kinds of guesses and assumptions.
In the modern world, this phenomenon has been widely publicized after the release of the movie “Da Vinci Code”. In this picture, the filmmakers drew the attention of a wide audience that the golden ratio is used and is found everywhere. It was mentioned there that proportion is respected everywhere, even in the human body. And of course, many people immediately became interested in this topic. The interest in the golden ratio that arose thanks to this film has not subsided so far. The Internet has filled 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 build a Fibonacci spiral
It is logical that having learned so much about this wonderful "curl", someone will probably want to create his own analogue with his own hand.
This is easy enough to do. It is enough to have a compass and a notebook in a cell or graph paper on hand (or a ruler that will help to build symmetrical, neat squares).
You need to start building a 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 be the beginning of the golden spiral. As the latter unwinds, an increasing number of proportional figures join it, until the desired spiral size is reached. The most important thing is to observe the rule where the length of the sides of each next square is always equal to the sum of the lengths of the sides of the two previous ones.
Golden rectangle
An ideal, from the point of view of the Fibonacci spiral, rectangle has sides whose length is proportional to each other precisely in terms of the phi coefficient. In other words, when dividing one side by the other, it must necessarily turn out to be 1.618 or 0.618 (the number inverse to the coefficient phi).
Such rectangles are quite common in architecture and composition. It is also interesting that it is their majority of people who consider them to be “ideal” or “right” 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 with dots or lines the main elements in the paintings and divide the canvas into many small Fibonacci rectangles, you can notice an interesting fact. On a huge number of works of art, 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 this is not surprising. The spiral reflects the law of nature itself, and she is a brilliant creator.
Some amazing and interesting facts.
- More recently, in social networks there was even a certain kind of fashion for pictures of girls who throw their hair back in water, getting a lot 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 influence of the golden ratio.
- It has long been known in metallurgy that alloys of various metals have better resistance properties if the specific gravity of the elements is related to each other according to the Phi coefficient.
- The proportions of various substances in hemoglobin are subject to this law.
- There is even an officially registered Golden Section Institute.
- In addition to the direct coefficient phi, there is also an inverse proportion to it, the number 0.618, which is also often used in various calculations.
Mankind received all the fundamental knowledge by observing the world around it. Over and over again, people noted patterns in changing seasons, found the relationship between thunder and lightning, studied the stars, and created calendars.
The law of the golden ratio is completely on the surface. And 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.
Exactly this way, according to the principle of the golden ratio, living organisms develop most harmoniously. Each next step is only the sum of the two previous ones. Each subsequent coil of the spiral grows gradually, opening more and more, but repeating the general direction.
This is one of the greatest laws of the universe.