Medieval Europe in the views of the average person is usually associated with the bonfires of the Inquisition, the Crusades, wars and blood. It would seem that there is no question of any science at this time. And yet, the two greatest discoveries come to us from this era - Arabic numerals and the Fibonacci sequence. There were, of course, other scientific discoveries, but now we will not talk about them.
Leaving aside the history of Arabic numerals, we will take a closer look at the Fibonacci sequence - what it is and what it is so famous for. In fact, the Fibonacci sequence is a series of numbers in which the senior member of the sequence equals the sum of the two nearest lower members of the sequence. As a result of such actions, the following numbers will be obtained:
1; 1; 2; 3; 5; 8; thirteen; 21 etc.
They are called Fibonacci numbers, and together they form a Fibonacci series. But the matter is not even in the numbers themselves, but in the relations between them. So, the ratio of the number in the sequence to the previous member of the sequence results in a value close to 1.618. And the larger the numbers used for such an attitude, the more accurately this value is respected.
Another, no less interesting fact that the Fibonacci sequence has is the relation of the previous member to the next. This ratio approaches 0.618 and is the reciprocal of 1.618.
If we take the ratio of other numbers from the Fibonacci sequence, not the closest, but, for example, through one or two, then the result will be different values: for members of the sequence taken through one, we will get a number tending to 2.618. When calculating the ratio of the senior term to the youngest through two members of the sequence, the result will tend to 4.236. If we consider, according to the same principle, the relations of the youngest members of the sequence to the senior ones (through one or two terms), then the opposite values will be obtained for the numbers already obtained: 0.382 (the inverse of the number 2.618), the next - 0.236 (the inverse of 4.236) and so on.
At first glance, this is all just curious information, a game of numbers that does not have practical implementation. However, this is not at all true. In technology, in art, in architecture, there is the concept of the golden section. It is the ratio of the parts of any object to each other, creating the most harmonious perception of the object as a whole. Very often, the golden ratio is used by artists and architects, seeking the impression of harmony from their paintings and structures. The same ratio is recommended to use photographers when composing the frame. One of the rules for frame composition is: to get a good picture, divide the frame into three parts and place the center of the composition at the intersection of the vertical and horizontal lines, which make up 2/3 of the horizontal and vertical frames. And the golden ratio is one of the Fibonacci ratios - 1.618. It is this ratio of parts and the whole that will provide the most harmonious perception. So, the Fibonacci sequence is not only a game of the mind, but it is also literally the foundation on which harmony and the beauty of perception of the world stand.
Fibonacci ratios are also true in wildlife. They can touch a variety of areas. So, the spiral-shaped snail shell also obeys Fibonacci ratios. Plant growth, the number of branches, leaves, their location are often also located in accordance with the numbers and Fibonacci ratios.
Well, the most famous use of Fibonacci numbers is in trading in financial markets. In the practice of traders, both the numbers that make up the Fibonacci sequence and the Fibonacci ratios are used. These coefficients are used to plan significant levels at which changes in price behavior can be expected.
In addition to the direct use of Fibonacci ratios , there are many other trading methods created using them. These include Fibonacci lines, Fibonacci zones, Fibonacci projections, etc. This helps traders predict market behavior, prepare in advance for possible changes in price behavior, and plan their trading.
All of the above does not cover all the manifestations of the influence of numbers and the Fibonacci sequence in science, technology, art, but gives an idea of what it is - the Fibonacci sequence.