The Fibonacci sequence.

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Medieval Europe in the representations the average person usually associated with the fires of the Inquisition, the Crusades, wars and blood.It would seem that about any science at this time and can be no question.And yet, two of the greatest discoveries come to us from that era - Arabic numbers and the Fibonacci sequence.There were, of course, other scientific discoveries, but now it goes about it.

Leaving aside the history of Arabic numerals, a closer look closely to the Fibonacci sequence - what it is, and what it is so famous.In fact, the Fibonacci sequence is a series of numbers, in which the senior member of the sequence is the sum of the next two junior members of the sequence.As a result of such actions will these numbers:

1;1;2;3;5;8;13;21, etc.

They are called Fibonacci numbers, and together they form the Fibonacci series.But it's not in the numbers but in the relations between them.Thus, the ratio of the number in the sequence of the previous members of the sequence results in a value of close to 1,618.And the figures used for this ratio, the more the closer adherence to this value.

Another, no less interesting fact, which has a Fibonacci sequence, is the attitude of the previous term to the next.This ratio is close to the value of 0.618 and is the reciprocal of 1.618.

If you take the attitude of the other numbers in the Fibonacci sequence, not the next, but, for example, through one or two, the result will be different values: for the members of the sequence, taken at one will obtain the number, tends to 2.618.In calculating the ratio of senior to junior member of the two members of the sequence, the result will strive to 4,236.If we consider the same principle attitude of younger members of the sequence for the elderly (over one or two members), you will get back the value already received numbers: 0.382 (the inverse of the number 2,618), the next - 0.236 (the inverse of 4.236) and so on.

At first glance, it's just interesting information, a numbers game that has no implementation.However, it is not so.In technology, in art, in architecture there is the concept of the golden section.He is the ratio of units of any article together, create the most harmonious perception of the object as a whole.Very often, the golden section are artists and architects, seeking from his paintings and constructions impression of harmony.The same ratio photographers recommend to use when building the frame.One of the rules states that the composition of the frame: to get a good picture frame Delhi into three parts and placed the center of the composition at the intersection of the vertical and horizontal lines that make up 2/3 of the horizontal and vertical frame.A golden section is one of the Fibonacci ratios - 1,618.It is the ratio of parts and whole provide the most harmonious perception.So, the Fibonacci sequence is not only a game of the mind, but is literally the foundation on which are harmony and beauty perception of the world.

Fibonacci ratios are also valid in nature.They can relate to many different areas.For example, snail shell, spiral-shaped, is also subject to the Fibonacci ratios.Height of plants, number of branches, leaves, their location is often also arranged according to the Fibonacci numbers and coefficients.

Well, the most famous use of Fibonacci numbers - to trade in the financial markets.In practice, traders are used as digits that make up the sequence of Fibonacci and the Fibonacci ratios.These coefficients are used for planning significant levels, which can be expected to change the behavior of prices.

addition to the direct use of the Fibonacci ratios, there are many other methods of trade, created with their use.These include the Fibonacci lines, Fibonacci zones, Fibonacci projections, etc.It helps traders to predict the behavior of the market, to prepare for possible changes in the behavior of prices and plan your trading.

All the above does not cover all forms of influence and numbers of the Fibonacci sequence in science, technology, the arts, but it gives an idea of ​​what it is - Fibonacci sequence.