SUMMACIONNAY FIBONACCI SEQUENCE
Release your imagination in free flight. Think about the Universe, the stars of our Galaxy. think about the beauty and form all sorts of natural wonders: oceans, trees, flowers, plants, animals and even microorganisms in the air we breathe. Point your thought on human achievements in areas such as science, theory, medicine, radio and television. You may be surprised to learn that in all these facilities is something common - summacionnay Fibonacci sequence. In the thirteenth century Thomas Aquinas formulated one of the basic principles of aesthetics - the feelings are pleasant objects with correct proportions. He referred to the direct link between beauty and mathematics, which often you can "measure" and found in nature. In the instincts of man laid positive reaction to correct geometrical forms as environmental nature and man-made objects such as paintings. Thomas Aquinas referred to the same principle, that opened the Fibonacci.
Mathematician Fibonacci lived in the twelfth century (1175). He was one of the most famous scientists of his time. Among his greatest achievements is the introduction of Arabic numerals instead of Roman. He opened the summacionnuu Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
This mathematical sequence occurs when, starting with 1, 1, the following number is obtained by adding the previous two. But why this sequence is so important?
This sequence of asymptotically (approaching slower and slower) seeks to some constant ratio. However, this ratio is irrational, i.e. is a number with an infinite unpredictable sequence of decimal digits in the fractional part. It cannot be expressed accurately. If any member of the Fibonacci sequence divided into prior to it (for example, 13:8), the result is a figure that varies around irrational values 1.61803398875 -- and by the time the superior, not reaching it. But even while spending Eternity, it is impossible to know the ratio exactly, to the last decimal digit. For the sake of brevity, we will bring it as 1.618.
Special names to this ratio began to give before Luca Pacioli (medieval mathematician) named him as the divine proportion. Among its modern names such as the Golden ratio, the Golden mean and the Attitude of the whirling squares. Kepler called it a ratio of one of the treasures of geometry". In algebra, it is generally accepted symbol of the Greek letter Phi (f = 1.618).
the Asymptotic behavior of a sequence, ringing its ratio of about irrational numbers f may become clearer if the show relationships of the first few members of the sequence. This example shows the relationship of the second member to the first, the third to the second, fourth to the third, and so on:
1:1 = 1.0000, fewer Fi on 0.6180
2:1 = 2.0000 that more fees at 0.3820
3:2 = 1.5000 that fewer Fi on 0.1180
5:3 = 1.6667, more Phi in 0.0486
8:5 = 1.6000 that fewer Fi on 0.0180
as we move on суммационной Fibonacci sequence every new member will share the following with more and more approaching to an unreachable F.
we will see Below that the individual numbers of суммационной Fibonacci sequence can be seen in the movements of prices for goods. Fluctuations ratios around the value of 1.618 the greater or lesser amount we find in the Elliott Wave theory, where they are described in Rule interchange. Subconsciously seeking divine ratio: it is necessary for the satisfaction of his needs in comfort.
When you divide any member of the Fibonacci sequence following it turns out just the opposite of the 1.618 value (1 : 1.618). But it is also very unusual, even remarkable phenomenon. Because the initial ratio - infinite fraction, this ratio should be no end.
Another important fact is that the square of any Fibonacci numbers is equal numbers in the sequence before it, multiplied by the number that appears after him, plus or minus.
5 = (3 x 8) + 1
8 = (5 x 13) - 1
13 = (8 x 21) + 1
Plus and minus constantly alternate. This is another manifestation of an integral part of the Elliott wave theory is called the rule of alternation. It States that the complex corrective wave alternate with simple, strong pulse wave with weak koppektivnymi waves, and so on.
the DIVINE PROPORTION, IN NATURE
Just amazing how many permanent can be calculated using the Fibonacci sequence, and how its members are in a great number of combinations. However, not be an exaggeration to say that this is not just a numbers game, and the most important mathematical expression of natural phenomena ever open. The examples below show some interesting applications of this mathematical sequence.
Pyramid in Giza
Many tried to unravel the secrets of the pyramids in Giza. Unlike other Egyptian pyramids is not a tomb, but rather an insoluble puzzle from numeric combinations. Great ingenuity, skill, time and work of the architects of the pyramid, they used when erecting an eternal symbol indicate the critical importance of the message that they wanted to pass on to future generations. Their era was dopis, доиероглифической and symbols were the only means of recording discoveries. The key to geometric-mathematical secret of the pyramids in Giza, so long the former for humanity for a mystery, in fact, was transferred to Herodotus temple priests, inform him that the pyramid was built so that the area of each of its faces was equal to the square of its height.
Area of triangle: 356 x 440 / 2 = 78320
the area of a Square: 280 x 280 = 78400
the Length of the side of the pyramid at Giza is 783.3 ft (238.7 m), height of the pyramid - 484.4 ft (147.6 ft). Edge length divided by height, leads to the ratio f=1.618. Height 484.4 feet corresponds 5813 inches (5-8-13) is the number of the Fibonacci sequence. These interesting observations suggest that the construction of the pyramid is based on the proportions f=1.618. Modern scholars tend to interpret that the ancient Egyptians built it with the sole purpose to convey the knowledge that they wanted to save for future generations. Intensive study of pyramids in Giza showed how extensive were in those days of learning in mathematics and astrology. In all internal and external parts of the pyramid number 1.618 plays a Central role.
Pyramid in Mexico
Not only the Egyptian pyramids are constructed in accordance with the perfect proportions of the Golden section, the same phenomenon was discovered and the Mexican pyramids. An idea that both Egyptian and Mexican pyramids were built around the same time, people of common ancestry. The cross-section of the pyramid are taking shape, similar to the stairs. In the first tier of 16 steps, in the second 42 degrees and in the third - 68 degrees. These numbers are based on the Fibonacci ratio as follows:
16 x 1.618 = 26
16 + 26 = 42
26 x 1.618 = 42
42 + 26 = 68
Number of f = 1.618 laid in the proportions of the Mexican pyramids. (Source: Mysteries of tНe Mexican рyramids, by рeter TНomkins /Peter Tomkins, "Secrets of the pyramids"/ (New York: Нагрег &USAID; Row, 1976) R. 246, 247.)
Another manifestation of Fibonacci numbers is observed among the sinuses on the stalk of the plant during its growth. The ideal scenario, you can see in the stems and flowers sneezewort'and. Each new branch grows from the sinuses and gives rise to other branches. If to consider together the old and the new branch, in each horizontal plane found a Fibonacci number. (Source: ТНе Divine рroрortion, by H. E. Нuntley /H. E. HUNTLEY, "divine proportion"/ (New York: Dover, 1970) R. 163.). Gold in the number of newly striking, when we study inflorescences asteraceous plants:
iris - 3 lobe
Primrose - 5 petals
A. artemisiifolia - 13 petals
Nivyanik ordinary -34 petal
Astra - 55 and 89 petals
the Number and location of flowers in a head of a representative of the Compositae are a great example of Golden numbers that are found in nature. We searched for laws that worked in the past and, therefore, is likely to continue to act in the future. In the face of Fibonacci ratios, we seem to have found such a law.
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