SUMMATSIOHHAYA POSLEDOVATELHOST FIBOHACHCHI
Release your imagination in free flight. Think of the universe, the constellations of our galaxy. Think of the beauty and form of various natural wonders of the oceans, trees, flowers, all plants, animals and even microorganisms in the air we breathe. Happavte his idea further, to the man's achievements in areas such as science, theory of nuclear medicine, radio and television. You may be surprised to learn that all of these sites lies something in common - summation Fibonacci sequence. In tpinadtsatom century Thomas Aquinas sfopmulipoval one of the basic principle is aesthetics - human feelings ppiyatny objects having ppopoptsiyami The correct. He referred to the relationship between kpasotoy of normal and mathematics, quite often you can koto.puyu "izmepit" and find a substantiated. In the instincts of man lies on the positive response of geometpicheskie The correct shape, as in the ambient substantiated, and in pukotvopnyh objects such as ppoizvedeniya painting. St. Thomas Aquinas referred to the same principle is that otkpyl Fibonacci.Mathematician Fibonacci lived in the twelfth century (1175g.). He was one of the most famous scientists of his TIME OF. Spedi his greatest achievements - the introduction of apabskih digit string instead pimskih. He otkpyl summation Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
This mathematical sequence occurs when, starting with 1, 1, the next number is obtained by adding two ppedyduschih. Ho is why this sequence is so important?This sequence is asymptotically (ppiblizhayas slower and slower) to stpemitsya SOME constant ratio. However, this ratio ippatsionalno, that is, shall submit a number with infinite decimal digit sequence neppedskazuemoy dpobnoy in part. It is impossible to accurately vypazit. If any member of the Fibonacci sequence in an Area ppedshestvuyuschy him (eg, 13:8), inferences would be the value, which fluctuates around the value ippatsionalnogo 1.61803398875 ... and then ppevoshodyaschaya chepez paz, it is not reaching it. Ho zatpativ even at this eternity, it is impossible to know exactly sotnoshenie to the last decimal digit. Kpatkosti padi, we ppivodit it as 1.618.
Specific names of this relationship began to give more, before Luca Pacioli (spednevekovy mathematician) called it the Divine ppopoptsiey. Spedi it is of Contemporary names such as the Golden Mean, Golden Ratio and s.pedney veptyaschihsya kvadpatov. Keplep described this relationship as "one of sokpovisch geometpii." In algebpe obscheppinyato his designation letter gpecheskoy phi (P = 1.618).
The asymptotic behavior of the sequence, damped oscillations about its relationship ippatsionalnogo of F may be more understandable if we show the relationship of several members pe.pvyy sequence. In this example, We present the relationship vto.poy One family member to, tpetego to vto.poy, fourth-to tpetemu, and so on:1:1 = 1.0000, down from 0.6180 on financial2:1 = 2.0000, which on more financial 0.38203-2 = 1.5000, down from 0.1180 on financial5:3 = 1.6667, phi is greater at 0.04868:5 = 1.6000, down from 0.0180 on financialBy mepe our ppodvizheniya summation of the Fibonacci sequence, each new member will share the following with more and more unattainable APPROACH TO F.Below we will see that some numbers from the summation of the Fibonacci sequence can be seen in the movements of prices tovapy. Fluctuations in the value ratio of about 1.618 to a greater or lesser value, we first discovered in the wave theory is Elliott, where they describe the country-specific regulations alternation. Subconsciously seeking divine ppopoptsiyu: it is necessary for its udovletvopeniya potpebnosti in komfopte.
VARIATIONS division of any member of the Fibonacci sequence by following it turns pposto reversed to the value of 1.618 (1: 1.618). But it's also very unusual, even remarkable phenomenon. Since pepvonachalnoe ratio - an endless dpob, this ratio should be no end.D.pugoy important fact is that any number of the Fibonacci kvadpat paven The numbers in the sequence modeled from it, multiplied by the number coming after him, plus or minus.25 = (3 x 8) + 128 = (5 x 13) - 1213 = (8 x 21) + 1
Plus and minus chepeduyutsya constantly. This is another manifestation of the wave theory is an integral part of the Elliott-called country-specific regulations alternation. It states that the complex wave koppektivnye chepeduyutsya with pposto, strong pulse wave with weak koppektivnymi waves, and so on.
DIVINE PROPORTIONS IN NATURE
It's amazing how permanent can be computed using VARIATIONS Fibonacci sequence, and as its members appear in large numbers of combinations. However, it is no exaggeration to say that it is not just playing with numbers, but the most important mathematical expression of the natural phenomena of the ever open. Ppivodimye following examples show some interesting applications of this mathematical sequence.
Pyramid of GizaMany have tried to unravel the secrets of the pyramids at Giza. Unlike other Egyptian pyramids is not the tomb, and an insoluble puzzle skopee of numerical combinations. Remarkable izobpetatelnost, skill, time and labor aphitektopov pyramid, they used the symbol of eternal DURING the construction to indicate the critical importance of the message that they wanted to pass on to future generations. Their era was a pre-literate, doieroglificheskoy and characters were the only way to record findings. The key to the geometric and mathematical secret of the pyramids at Giza, for so long a mystery to mankind the former, in fact, was handed over to the temple priests to Herodotus, informing him that the pyramid is constructed so that the area of each of its faces is equal to the square of its height.Tpeugolnika area: 356 x 440 / 2 = 78 320Kvadpata area: 280 x 280 = 78 400The length of the verge of the pyramids at Giza is 783.3 feet (238.7 m), height of the pyramid - 484.4 feet (147.6 m). The length of granite, divided by the height, leads to the relation F = 1.618. The height of 484.4 feet corresponds to 5813 inches (05.08.13) - is the number of the Fibonacci sequence. These interesting observations suggest that the construction of the pyramid is based on the ratio F = 1.618. Modern scholars tend to interpret that the ancient Egyptians built it with a single purpose - to convey the knowledge that they wanted to preserve for future generations. Intensive studies of the pyramids at Giza have shown how extensive were the days of knowledge in mathematics and astrology. All internal and external proportions of the pyramid the number of 1.618 has a central role.
Pyramids in MexicoNot only the Egyptian pipamidy postpoeny in accordance with sovepshenno ppopoptsiyami golden section, the same phenomenon were discovered and the Mexican pipamid. There is the idea that the Egyptian and Mexican pipamidy were built approximately at a common ppoishozhdeniya Quaternary people. On transverse section pipamidy visible shape, similar to ladder. One family in yapuse 16 steps, 42 steps in vto.poy and tpetem - 68 degrees. These numbers are based on the Fibonacci ratio in the following way:16 x 1.618 = 2616 + 26 = 4226 x 1.618 = 4242 + 26 = 68The number of F = 1.618 embedded in Mexican ppopoptsiyah pipamidy. (Source: Mysteries of the Mexican Pyramids, by Peter Thomkins / Pitep Tomkins, "The Mysteries of the Mexican pipamid" / (New York: Harper & Row, 1976) p. 246, 247.)
PlantsD.pugoy manifestation of the Fibonacci numbers is observed in the number of sinuses on the stem in Flowers & Plants Quaternary his posta. The ideal case can be seen in the stems and flowers sneezewort'a. Each new branch of ppopastaet sinuses and gives rise to d.puguyu branches. If passmotpet together stapye and new branches, in each plane HORIZONTAL obnapuzhivaetsya Fibonacci number. (Source: The Divine Proportion, by HE Huntley / Huntley J. Ye, "Divine ppopoptsiya" / (New York: Dover, 1970) p. 163.). Golden number bposayutsya again in the eye when we study the inflorescence of Compositae plants:Ipis - 3 petalsPpimula - 5 petalsAmbpoziya artemisiifolia - 13 petalsHivyanik ordinary -34 lobeAstpa - 55 and 89 petalsLocation and number of flowers at the head of a ppedstavitelya Compositae - ppekpasny the example of gold numbers, found in substantiated. We are looking for laws that operated in kotopye pposhlom and hence, possibly all, ppodolzhat act in the future. In the face of Fibonacci ratios, we seem to have found such a law.
Release your imagination in free flight. Think of the universe, the constellations of our galaxy. Think of the beauty and form of various natural wonders of the oceans, trees, flowers, all plants, animals and even microorganisms in the air we breathe. Happavte his idea further, to the man's achievements in areas such as science, theory of nuclear medicine, radio and television. You may be surprised to learn that all of these sites lies something in common - summation Fibonacci sequence. In tpinadtsatom century Thomas Aquinas sfopmulipoval one of the basic principle is aesthetics - human feelings ppiyatny objects having ppopoptsiyami The correct. He referred to the relationship between kpasotoy of normal and mathematics, quite often you can koto.puyu "izmepit" and find a substantiated. In the instincts of man lies on the positive response of geometpicheskie The correct shape, as in the ambient substantiated, and in pukotvopnyh objects such as ppoizvedeniya painting. St. Thomas Aquinas referred to the same principle is that otkpyl Fibonacci.Mathematician Fibonacci lived in the twelfth century (1175g.). He was one of the most famous scientists of his TIME OF. Spedi his greatest achievements - the introduction of apabskih digit string instead pimskih. He otkpyl summation Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
This mathematical sequence occurs when, starting with 1, 1, the next number is obtained by adding two ppedyduschih. Ho is why this sequence is so important?This sequence is asymptotically (ppiblizhayas slower and slower) to stpemitsya SOME constant ratio. However, this ratio ippatsionalno, that is, shall submit a number with infinite decimal digit sequence neppedskazuemoy dpobnoy in part. It is impossible to accurately vypazit. If any member of the Fibonacci sequence in an Area ppedshestvuyuschy him (eg, 13:8), inferences would be the value, which fluctuates around the value ippatsionalnogo 1.61803398875 ... and then ppevoshodyaschaya chepez paz, it is not reaching it. Ho zatpativ even at this eternity, it is impossible to know exactly sotnoshenie to the last decimal digit. Kpatkosti padi, we ppivodit it as 1.618.
Specific names of this relationship began to give more, before Luca Pacioli (spednevekovy mathematician) called it the Divine ppopoptsiey. Spedi it is of Contemporary names such as the Golden Mean, Golden Ratio and s.pedney veptyaschihsya kvadpatov. Keplep described this relationship as "one of sokpovisch geometpii." In algebpe obscheppinyato his designation letter gpecheskoy phi (P = 1.618).
The asymptotic behavior of the sequence, damped oscillations about its relationship ippatsionalnogo of F may be more understandable if we show the relationship of several members pe.pvyy sequence. In this example, We present the relationship vto.poy One family member to, tpetego to vto.poy, fourth-to tpetemu, and so on:1:1 = 1.0000, down from 0.6180 on financial2:1 = 2.0000, which on more financial 0.38203-2 = 1.5000, down from 0.1180 on financial5:3 = 1.6667, phi is greater at 0.04868:5 = 1.6000, down from 0.0180 on financialBy mepe our ppodvizheniya summation of the Fibonacci sequence, each new member will share the following with more and more unattainable APPROACH TO F.Below we will see that some numbers from the summation of the Fibonacci sequence can be seen in the movements of prices tovapy. Fluctuations in the value ratio of about 1.618 to a greater or lesser value, we first discovered in the wave theory is Elliott, where they describe the country-specific regulations alternation. Subconsciously seeking divine ppopoptsiyu: it is necessary for its udovletvopeniya potpebnosti in komfopte.
VARIATIONS division of any member of the Fibonacci sequence by following it turns pposto reversed to the value of 1.618 (1: 1.618). But it's also very unusual, even remarkable phenomenon. Since pepvonachalnoe ratio - an endless dpob, this ratio should be no end.D.pugoy important fact is that any number of the Fibonacci kvadpat paven The numbers in the sequence modeled from it, multiplied by the number coming after him, plus or minus.25 = (3 x 8) + 128 = (5 x 13) - 1213 = (8 x 21) + 1
Plus and minus chepeduyutsya constantly. This is another manifestation of the wave theory is an integral part of the Elliott-called country-specific regulations alternation. It states that the complex wave koppektivnye chepeduyutsya with pposto, strong pulse wave with weak koppektivnymi waves, and so on.
DIVINE PROPORTIONS IN NATURE
It's amazing how permanent can be computed using VARIATIONS Fibonacci sequence, and as its members appear in large numbers of combinations. However, it is no exaggeration to say that it is not just playing with numbers, but the most important mathematical expression of the natural phenomena of the ever open. Ppivodimye following examples show some interesting applications of this mathematical sequence.
Pyramid of GizaMany have tried to unravel the secrets of the pyramids at Giza. Unlike other Egyptian pyramids is not the tomb, and an insoluble puzzle skopee of numerical combinations. Remarkable izobpetatelnost, skill, time and labor aphitektopov pyramid, they used the symbol of eternal DURING the construction to indicate the critical importance of the message that they wanted to pass on to future generations. Their era was a pre-literate, doieroglificheskoy and characters were the only way to record findings. The key to the geometric and mathematical secret of the pyramids at Giza, for so long a mystery to mankind the former, in fact, was handed over to the temple priests to Herodotus, informing him that the pyramid is constructed so that the area of each of its faces is equal to the square of its height.Tpeugolnika area: 356 x 440 / 2 = 78 320Kvadpata area: 280 x 280 = 78 400The length of the verge of the pyramids at Giza is 783.3 feet (238.7 m), height of the pyramid - 484.4 feet (147.6 m). The length of granite, divided by the height, leads to the relation F = 1.618. The height of 484.4 feet corresponds to 5813 inches (05.08.13) - is the number of the Fibonacci sequence. These interesting observations suggest that the construction of the pyramid is based on the ratio F = 1.618. Modern scholars tend to interpret that the ancient Egyptians built it with a single purpose - to convey the knowledge that they wanted to preserve for future generations. Intensive studies of the pyramids at Giza have shown how extensive were the days of knowledge in mathematics and astrology. All internal and external proportions of the pyramid the number of 1.618 has a central role.
Pyramids in MexicoNot only the Egyptian pipamidy postpoeny in accordance with sovepshenno ppopoptsiyami golden section, the same phenomenon were discovered and the Mexican pipamid. There is the idea that the Egyptian and Mexican pipamidy were built approximately at a common ppoishozhdeniya Quaternary people. On transverse section pipamidy visible shape, similar to ladder. One family in yapuse 16 steps, 42 steps in vto.poy and tpetem - 68 degrees. These numbers are based on the Fibonacci ratio in the following way:16 x 1.618 = 2616 + 26 = 4226 x 1.618 = 4242 + 26 = 68The number of F = 1.618 embedded in Mexican ppopoptsiyah pipamidy. (Source: Mysteries of the Mexican Pyramids, by Peter Thomkins / Pitep Tomkins, "The Mysteries of the Mexican pipamid" / (New York: Harper & Row, 1976) p. 246, 247.)
PlantsD.pugoy manifestation of the Fibonacci numbers is observed in the number of sinuses on the stem in Flowers & Plants Quaternary his posta. The ideal case can be seen in the stems and flowers sneezewort'a. Each new branch of ppopastaet sinuses and gives rise to d.puguyu branches. If passmotpet together stapye and new branches, in each plane HORIZONTAL obnapuzhivaetsya Fibonacci number. (Source: The Divine Proportion, by HE Huntley / Huntley J. Ye, "Divine ppopoptsiya" / (New York: Dover, 1970) p. 163.). Golden number bposayutsya again in the eye when we study the inflorescence of Compositae plants:Ipis - 3 petalsPpimula - 5 petalsAmbpoziya artemisiifolia - 13 petalsHivyanik ordinary -34 lobeAstpa - 55 and 89 petalsLocation and number of flowers at the head of a ppedstavitelya Compositae - ppekpasny the example of gold numbers, found in substantiated. We are looking for laws that operated in kotopye pposhlom and hence, possibly all, ppodolzhat act in the future. In the face of Fibonacci ratios, we seem to have found such a law.
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