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ریاضی به زبان ساده - Fibonacci number sequence and golden
تاریخ : 1388/10/29 | 18:34 | نویسنده : Mahta
Fibonacci number sequence and golden







Italian Leonardo Fibonacci died around the year 1200 issue will plan: Suppose that a pair of male and female rabbits at the end of every month a new pair of male and female rabbits born to bring ... If no rabbit initiated between the end of a year is a pair of rabbits?

Fibonacci decided to calculate the number of their numbers Fn months N pairs at the beginning of my Re.

After F1 = 1 and F2 = 2 will be ... Since the start of the first month there is only one original pair ... but starting the second month the first pair of the second pair of true principles.

She then noticed that I started months N pairs are divided into two groups: Fn-1 Total number of pairs of old and new pairs of N-1 month. Because the new pair is produced after a month and after a month produces the first pair ... Number of new pairs to the number of pairs of two months ago with Fn-1 is shown.

After:

Fn = Fn-1 Fn-2

Using this formula and basic values of F1 = 1 and F2 = 2 be the number of pairs obtained after a year and write F12 = 233.

Fn series of numbers called Fibonacci sequence. A general agreement with values of 1 and 1 instead of the primary 1 and 2 starts (so that the sequence of the following are written)

... , 1,1,2,3,5,8,13,21,34,55,89,144,233

Now, if the sequence number to each number divided Qblysh we will have a Urinary series:

1 / 1 = 1, 2 / 1 = 2, 3 / 2 = 1? 5, 5 / 3 = 1? 666 ... 8 / 5 = 1? 6, 13 / 8 = 1? 625, 21/13 = 1? 61,538 and ...

Breymann opinion that everything forward when you reach to a special number. This topic to better chart below:

We call this number the golden number almost equal to that of this number is: ... 1.618033

In other words the number of sequence looks golden:

  
Fibonacci series in nature:

Now, Miami and another to look at the sequence: If we square the two sides together in a Bgzarym and above a square with sides 2 Endo Bgzarym and the way out ... We will have a form like the form below:

This rectangle known as the Fibonacci rectangles. Now if these points form a connected we reach as follows:

This form can be similar in nature and following vision:

Other examples of sequence in nature can Aftabgrdn flower seeds or flowers, some pointed petal number (For more information see here or here).

Golden number

How to obtain already golden number was speaking through Fibonacci sequence. Now about other ways to obtain this number we speak ...

Artists in ancient times as well as Greek mathematicians knew rectangular beauty of art that the width and length X 1 was the rectangular square each time to remove 1 side open to the same rectangle with the same ratios remain the main rectangle.

Because rectangle line width and length of 1-X is 1 when compared with Zlhay two rectangles are equal:

Now if the above equation for X can be resolved positive root equation is the golden number:

Maths this number in the world with signs Greek

  
(Called Phi) are show ... (For more information on this page to the golden number or page or see this page)

Use this number:

Pyramid "Reem Papyrus" in the pyramid Slash one of the oldest examples of the use of this number in making Bnahast ...

If within one Shalhay on the distance the tip of the pyramid pyramid pyramid floor to the middle point of division 1.6 we will answer ...

Archaeologists are not sure whether the work done or intend to have happen!

Another interesting subject is that if the diameter of the pyramid twice its height divided we answer the number Pi (3.14) will be.

Another example is building Parthenon in Greece. To build the 440 BC This building made of golden rectangles are used:

Following the map you can see this building ... Try site during each of the box when the form explaining the division within it are achieved golden number?

How to draw a golden rectangle:

To draw a golden rectangle first square side Beck desired shape in the middle, then pulled down side of this square to find. After an arc with a beam radius as the middle square to draw right corner is known as long rectangle.

Other use of this number:

- Whenever you individually during the wide divide it matter how this number is closer to the golden number is the person Bahvshtr. (This has not been established ... For more information, see here!)

- Length Hrs·h one finger knuckle to get the desired size. Size of the upper middle divide. Number about 1.6, not? In the above action (specify ratio) in the middle of a small section to do. Answer?

- Mtvan value through the following numbers to two decimal places of precision achieved:

At this website you golden number to fifty thousand decimal places to visit!!

Site and complete in number Jaml golden! (Sure is recommended)

This is an article I!

http://riazichi.com/content-4.html



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