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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