[數學][文章]Fibonacci Numbers and Nature

[數學][文章]Fibonacci Numbers and Nature

yll 於 星期四 二月 27, 2003 11:04 pm


Fibonacci Numbers and Nature
值得一看 耍酷
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
看見一個需要,並用數學解決它!

yll
帥哥良~
帥哥良~
 
文章: 4368
註冊時間: 2002-08-28
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SCTT 於 星期三 三月 12, 2003 11:32 pm


板主!這個網站的網址是什麼!我需要!

SCTT
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yll 於 星期四 三月 13, 2003 12:39 am



yll
帥哥良~
帥哥良~
 
文章: 4368
註冊時間: 2002-08-28
來自: 天父的小花園~

神乎其技 於 星期四 五月 15, 2003 9:30 pm


內容蠻豐富ㄉ

神乎其技
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scsnake 於 星期四 五月 15, 2003 9:37 pm


我好像已前看過∼

scsnake
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--- 於 星期四 五月 15, 2003 10:12 pm


直線L: y = (1+sqrt(5))/2 * x

Let's start at the origin and work up the line.
The first is (0,0) of course, so here ARE two integers i=0 and j=0 making the point (i,j) exactly on the line! In fact ANY line y=kx will go through the origin, so that is why we will ignore this point as a "trivial exception" (as mathematicians like to put it).
The next point close to the line looks like (0,1) although (1,2) is nearer still. The next nearest seems even closer: (2,3) and (3,5) even closer again. So far our sequence of "integer coordinate points close to the Phi line" is as follows: (0,1), (1,2), (2,3), (3,5)
What is the next closest point? and the next? Surprised? The coordinates are successive Fibonacci numbers!
Let's call these the Fibonacci points. Notice that the ratio y/x for each Fibonacci point (x,y) gets closer and closer to Phi=1·618... but the interesting point that we see on this graph is that the Fibonacci points are the closest points to the Phi line

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--- 於 星期四 五月 15, 2003 10:24 pm


Cycles in the Fibonacci numbers
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Here are some patterns people have already noticed:

There is a cycle in the units column - the cycle of units digits (0,1,1,2,3,5,8,13,21,34,55,...) repeats from n=60 and again every 60 values.

There is also a cycle in the last two digits, repeating (00, 01, 01, 02, 03, 05, 08, 13, ...) from n=300 with a cycle of length 300.

For the last three digits, the cycle length is 1,500
for the last four digits,the cycle length is 15,000 and
for the last five digits the cycle length is 150,000

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--- 於 星期四 五月 15, 2003 10:29 pm


Initial digit frequence in the Fibonacci numbers
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費氏數列ㄉ第一位數字:

前100ㄍ費氏數列ㄉ第一位數字:

Digit: 1 2 3 4 5 6 7 8 9
Frequency: 30 18 13 9 8 6 5 7 4 100 values
Percent: 30 18 13 9 8 6 5 7 4
----------------------------

前10000ㄍ費氏數列ㄉ第一位數字:

Digit: 1 2 3 4 5 6 7 8 9
Percentage: 30 18 13 10 8 7 6 5 5

請解釋其分配比例!

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E.T 於 星期六 六月 21, 2003 11:42 pm


meow ~ the answer is ... ?
Click this : [>> 有趣的科學(Science's World) <<]

Let's go to discuss ~*

左鍵: 點擊縮放; 右鍵: 觀看原圖左鍵: 點擊縮放; 右鍵: 觀看原圖左鍵: 點擊縮放; 右鍵: 觀看原圖左鍵: 點擊縮放; 右鍵: 觀看原圖

E.T

 
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註冊時間: 2003-03-29
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