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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 var   i , n : Longint ; { } function Fib ( X : Byte ) : Longint ; var   s , n1 , n2 : Longint ; begin   fib := 1 ;   if x< 3 then     exit;   n1 := 1 ; n2 := 1 ;   while x> 2 do   begin     dec ( x ) ;     s := n2 + n1;     webrtc n1 := n2;     n2 := s;   end ;   fib := S; end ; { } begin   readln ( n ) ;   if n< = 1 then     exit;   i := 1 ;   repeat     write ( fib ( i ) , ' ' ) ;     inc ( i )   until     fib ( i ) > = n; end . 1
  : 17.10.2009 : 5,816 : 7664 ( 2558 )
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This sequence tends to a constant mathscinet ratio. Let

A series of numbers called the Fibonacci sequence is known to all of the film "The Da Vinci Code." Has been described as a puzzle medieval Italian mathematician Leonardo of Pisa, better known as Fibonacci (Fibonacci - son of Bonacci), in the XIII century.
The sequence is as follows: mathscinet 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ..... It can continue indefinitely, but the point is that each successive number is the sum of the previous two. By itself, the sequence would not be interesting if it were not for its interesting mathematical properties.
This sequence tends to a constant mathscinet ratio. Let's take a hand calculator and feel like pioneers, performing simple calculations. Results can be written to within thousandths. So divide 13 by 8, 21, 13, 34 to 21, 55 to 33 (ie, each number in a sequence number that precedes it). All the numbers fluctuate about the number 1,618, surpassing by paz then, it is not reaching it. Now divide sequentially mathscinet 8 13, 13 21, 21 34, 34 55. This attitude of each previous number to the next similarly close to the number 0,618. Divide 1 to 0,618. We get 1,618, so our numbers are inversely proportional. If we divide the elements of the sequence by one, we get the number 2,618 and 0,382, which are also inversely proportional. This is the so-called Fibonacci ratios.
Why all these changes? So we come to one of the most mysterious phenomena of nature, which is called mathscinet the Golden Section. The golden section is widely used since ancient mathscinet times in architecture and painting, and the very nature of the miraculous "applies" in the creation of its living organisms, the golden section. But back to the Fibonacci numbers. Here you can watch movies on this remarkable sequence: Watch >> Watch >>
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On price charts, this behavior is reflected in the classic lines of resistance - support, channels,

The Fibonacci sequence Fibonacci lines
Great Fibonacci in every sense! The Fibonacci sequence - it's idt mysticism market "Forex". idt The great thing that the psychological processes of the human subconscious mind realized, even in this, there is little predictability of how the forex market! In a statistical analysis of the market ("technical analysis") idt are almost certain idt psychological processes of crowd behavior.
On price charts, this behavior is reflected in the classic lines of resistance - support, channels, trends, idt etc. "Formula" for success. Resistance line support, as we know, reflect a balance of supply and demand made on the market, at a fixed time. It is assumed that in the future, idt when the market reaches the specified price, traders might try to stay on the laurels price level, ie, when moving to a line of resistance-support "from above", will attack her shopping, and "from below" - sales!
But what to do in those fairly frequent cases where prices have gone far beyond the range of volatility? Then the assumptions for the prediction based on the following ideas: if the market for a long time buy, so you can build a Fibonacci line from the closing price of warrants bay at the beginning," to the closing price of warrants bay at the end of the path." Since the Fibonacci lines are stable numerical ratio sequence numbers, then the resistance line support, psychologically, will fit, just these levels! Most importantly - know it all traders, and of course, so really, in practice, Fibonacci lines are a good guide for building a strategy of buying and selling currencies?
How to do this in practice? You choose the menu treyderskoy software (trading platform), such as MT4 menu icon in the tool Fibonacci and set the cursor to the highest (or lowest, depending on the direction of the current trend) candle (closing price). Then "drag" the cursor to the very bottom (top) candle (closing price). idt Some traders recommend the use of the maximum or minimum prices, but still more than the closing price of "important." So you got to the levels idt of analysis and installation of Stop and Profit is 23.6, 38.2, 50.0, 61.8, 100. Why these? Because the levels are formed by the following calculation: the Fibonacci sequence fragment idt is taken (eg 8,13,21) and the first element is divided into the following two amounts - were 0.2364, followed by the first partition on the second (or the second to the third) - were 0.618 ("golden section "), idt and further on the same principles. The more and more elements from the beginning of the sequence, the more accurate the results. That's it! You can make predictions and look for an entry point into the market! idt
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The Fibonacci sequence, known to all in the film

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The Fibonacci sequence, known to all in the film "The Da Vinci Code" - a series nature magazine of numbers, as described in the form of riddles Italian mathematician nature magazine Leonardo of Pisa, better known by his nickname Fibonacci, in the XIII century. In short the essence of mystery: Someone placed a pair of rabbits in a certain confined space, to see how many pairs of rabbits will be born at the same time throughout nature magazine the year, if the nature nature magazine of rabbits is that every month a pair of rabbits gives birth to another nature magazine couple, and the ability to produce offspring with They appear to reach two months of age. The result is a sequence of 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, where display number comma pairs of rabbits in each of the twelve months. This sequence can be continued indefinitely. Its essence is that each successive number is the sum of the previous two.
In this sequence, there are a number of mathematical features nature magazine that are sure to touch. This sequence is asymptotically (approaching slower and slower) tends to a constant ratio. However, this ratio is irrational, nature magazine then there is a number with an infinite, unpredictable sequence of decimal digits in the fractional part. It can not be expressed nature magazine exactly. So the ratio of any term of the sequence to the preceding nature magazine number is around 1,618, a paz is excellent, it is not reaching it. The following similar approaches the number of 0,618, which is inversely proportional to 1,618. If we divide the elements of the sequence by one, we get the number 2,618 and 0,382, which are also inversely proportional. This is the so-called Fibonacci ratios. nature magazine What is all this? So we come to one of the most mysterious phenomena of nature. Fibonacci in fact not discovered anything new, it just reminded the world of the phenomenon called the Golden Section, which is not inferior to the significance of the Pythagorean theorem. All objects around us, we distinguish between including and form. We like some more, some less, some do push glance. Sometimes interest may be dictated by the situation in life, and sometimes the beauty of the observed object. Symmetrical and proportional form, promotes the best visual perception and evokes a sense of beauty and harmony. The whole image is always consists of parts of different sizes in a specific ratio to each other and the whole. Golden ratio - the highest manifestation of the perfection of the whole and its parts in science, art and nature. If a simple example, the Golden Section - this division of the interval into two parts in such a ratio in which most applies to lower their sum (full line) to the most. If we take the entire length of c to 1, then a segment will be equal to 0.618, the length b - 0,382, so only condition is met Golden Mean (0.618 / 0.382 = 1.618, 1/0, 618 = 1,618). The ratio of c to a is equal to 1.618, but with a b 2,618. It's all the same, we are already familiar, the Fibonacci ratios. Of course there is the golden rectangle, the golden triangle, and even a golden cuboid. The proportions of the human body in many ratios are close to the Golden Section. Image: marcus-frings.de But the fun begins when we combine this knowledge. The figure clearly shows the relationship between the Fibonacci sequence and the golden ratio. We start with two squares of the first size. Add on top of the square of the second dimension. Paint on the next square nature magazine with sides equal to the sum of the previous two parties, nature magazine a third the size. By analogy, there is a square of the fifth dimension. And so on until you get bored, as long as the length of each side of the next square was equal to the sum of the lengths of the sides of the two previous ones. We see a series of rectangles, the length of the sides, which are Fibonacci numbers, and, if not strange, they are called Fibonacci rectangles. If we draw a smooth line through the corners of our squares, we get nothing but a spiral of Archimedes, which is always increasing spacing evenly. Sound familiar? Photo: ethanhein on Flickr and not only in clam shell can find the Archimedean spiral, and in many plants and flowers, they're just not as obvious. Aloe Multivalent: Photo: brewbooks nature magazine on Flickr Romanesco Broccoli: Photo: beart.org.uk nature magazine Sunflower: Photo: esdrascalderan on Flickr Pinecone: Photo: mandj98 on Flickr And if you look a little further away, you can see the Fibonacci sequence in the unattainable galaxies. nature magazine And then it's time to acces

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Fibonacci Sequence Fibonacci Sequence (Fibonacci Sequence) in trading on the open financial markets (including the retail forex market) is called technical analysis tool that is used to predict the price movements of different investment assets. From a mathematical point of view, it was built by the Italian mathematician Leonardo Fibonacci sequence of related numbers, which uses the so-called "golden ratio" or "golden ratio". In the Fibonacci sequence each successive number ndt is equal to the two preceding scrip. A subsequent private and the previous number tends to 0.618. The use of this number series to predict the behavior of the Forex market, where trends ndt are cyclical, and courses are subject to bouts followed ndt Pullback, was made possible thanks to the hypothesis that the financial markets are inherent properties of natural processes, the development of which is held under the laws of the "golden ndt section". It should be noted that the method based on the rule of division into "golden" proportions, allows you to search the values of real-valued function on a particular segment. Therefore, ndt this method is quite applicable in the analysis of the situation on the forex to find points of price extremes for a given timeframe. This is very important in determining the entry points. In addition, the Fibonacci sequence is effective for calculating the probability of repetition of market movement. The calculation of this sequence to a trained specialist is not that difficult, but it may take some time. In strict terms of operational decision-making trade to identify the above-described series of numbers it makes sense to use the potential of information and POS terminals. In most of them are integrated into the program of calculation using the Fibonacci indicator. Its use significantly speeds up and simplifies the process of analysis.
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Microsoft SDE -> Intel algorithmist -> Skype SDET 2 B.Sc - > M.Sc -> B.Psy -> Scrum Master -> Research Assistent ­https://www.youtube.com/user/igorkle1?feature=mhee fisher scientific ­http://igor-eta.livejournal.com/ ­http://www.idea2site.com/
f(n) = af(n-1) + bf(n-2) x^2 - ax - b. A1 A2 - , , . A1 A2 , f(n) = C1*A1^n + C2*A2^n, C1 C2 C1*A1 + C2*A2 = f(1), C1*A1^2 + C2*A2^2 = f(2). A1 = A2 = A, f(n) = C1*A^n + n*C2*A^n, C1 C2 C1*A + C2*A = f(1), C1*A^2 + 2*C2*A^2 = f(2).
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f(n) = af(n-1) + bf(n-2) x^2 - ax - b. A1 A2 - , , . A1 A2 , f(n) = C1*A1^n + C2*A2^n, C1 C2 C1*A1 + C2*A2 = f(1), C1*A1^2 + C2*A2^2 = f(2). A1 = A2 = A, f(n) = C1*A^n + n*C2*A^n, C1 C2 C1*A + C2*A = f(1), C1*A^2 + 2*C2*A^2 = f(2). , " " - ___________ fisher scientific
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LiveJournal Home Create an account Explore Search by Interest vile Search by School Community Direc

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Carl, Clara, and Fibonacci numbers: a poem, which is not the end of the Fibonacci numbers - it's such a sequence in which each successive number is the sum of the two preceding vile numbers. That is, if the first take-1, then it is 0 +1 = 1, then - 1 +1 = 2, then 2 +1 = 3, then 3 2 = 5 and later 5 +3 = 8 5 8 further = 13, and there are already 13 +8 = 21 and so on. It is clear, right? Carl Clara stole corals and Clara Carl stole the clarinet ... Everyone knows this tongue twister. But not everyone knows that in the Soviet journal "Pioneer" for 1987 ( 9) was a continuation of this tragic story, too, in the verse, and our heroes have become kinder and to engage in their noble deeds is the Fibonacci numbers. The magazine verse ends with the line in which the next number to 21. As you know, we are in the verses that he likes zarifmuem. One day, as you know, I even odnogruppnitsy control on medicine written in verse. And now my friend and carminative dzmitrykashlach, known stihoslozhitelem, decided vile to continue this poetic sequence that was interrupted more than a quarter century ago. We wrote his rhymed lines at a time and come down to just a twentieth of the Fibonacci series, but it took effort not less than the cost of our heroes. But just see what we have! Carl Clara stole corals and Clara Carl stole the clarinet ... (Hereinafter - the poetry of the journal "Pioneer") Once Clara gave him a box of hand soap; thought, Karl sent an answer to empty a bag of chocolates. Then soften Clara sent two balloons, But Charles had sent her, kinder, three new card suit of clubs. And thanks to Clare came five mittens vile single, as a symbol of friendship Karl in response Sends eight different sandals. Deeply moved, sent Clara Thirteen pipes for the samovar, and with tears in Charles sent ... Twenty-one knee shaft. Now - co-creation and dzmitrykashlach incopolis: Happy Clara parcel vile collected 34 pounds of fat. Carl was not in debt to Clara: From left post 55 lobsters. 89 milk chocolates Clara packs in dense cake. Charles can not be caught by surprise: 144 sent her cakes. Wondering Clara, but soon found two hundred and thirty-three vile left sock. (233) Seven times eleven vile and three times on one of Crispy wafers sent sheets. (377) Double-three hundred and ten pounds off from the courier. vile Will arrive in the afternoon. (610) Thirteen subtracted from thousands of pots - Balance left with the icebreaker "Sedov". vile (987) Forty-two (minus three) Sent Clara ceremonial pants. (1,597) Karl sent in a van cans - Two thousand and five hundred eighty-four. All day long labored maid - No more space Clara in the apartment. (2,584) Clara went on wholesale basis and ordered Charles to send a total number of ripe watermelons at once - The cube sixteen plus vosemsyat five. (4,181) Carl is in retaliation decided to send beads - All night long he continued to believe in the shipping carton and carved "Sixty-seven hundred sixty five" (6.765) In this our heroes in exhaustion ceased to send their gifts. Evil tongues say that they just felt sorry for sending the money, and the limit on the value of the received parcels of 120 euros a month without having to pay for customs clearance in Belarus so far no one has repealed. And the song does not end! Connect the wonderful Mary prosto_marija, slightly, however, breaking the rhythm: Clara loved Charles for dinner I sent two biscuits vile plus nine hundred and twelve dozen. (10.946), vile who will take up about 17,711 lines of writing? It seems pretty simple little number came out, it's easy rhyme.
Uh, under the latest chetyrehstishiyami I do not subscribe (libel and perjury!): Charles I as much money never given. But maybe someone of prochitateley this post wants to continue stihoryad?
Continue, continue on!
And what about the sequences in our game was a mystery: What will end this sequence? By B Z Uh ...? Mind you, not google!
Clara loved Charles for dinner I sent two biscuits plus nine hundred and twelve dozen. (10946)