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hola, randallfly here

If you know anything about me at all, you know there's nothing
I like more than numbers, and, especially, the Fibonacci Numbers.

Leonardo Fibonacci discovered the series in the 12th century:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, . . .

Phi = 1.6180339887... and goes on forever without repeating (like pi)

Phi is an irrational number -
it cannot be expressed as a fraction.
Here are the first 1,000 numbers of phi:

1.6180339887498948482045868343656381177 2030917980576286213544862270526046281890 2449707207204189391137484754088075386891 75212663386222353693179318006076672635 4433389086595939582905638322661319928290 26788067520876689250171169620703222104 32162695486262963136144381497587012203 4080588795445474924618569536486444924104 4320771344947049565846788509874339442212 54487706647809158846074998871240076521 70575179788341662562494075890697040002812 1042762177111777805315317141011704666 59914669798731761356006708748071013179 5236894275219484353056783002287856997829 7783478458782289110976250030269615617002 50464338243776486102838312683303724292 675263116533924731671112115881863851331 620384005222165791286675294654906811317 159934323597349498509040947621322298101 726107059611645629909816290555208524790 352406020172799747175342777592778625619 432082750513121815628551222480939471234 145170223735805772786160086883829523045 926478780178899219902707769038953219681 986151437803149974110692608867429622675 7560523172777520353613936

here's some schnizzle that will dazzle your brain:

1/89 is a repeating decimal fraction with 44 characters:  
.01123595505617977528089887640449438202247191

you can see the beginning of the Fib Numbers in the first 6 digits of 1/89

If you take each Fibonacci number, divide it by 10 raised to the power of its position in the Fibonacci sequence and add them all together, you get 1/89

0 / (10 ^ 1 ) +
1 / (10 ^ 2 ) +
1 / (10 ^ 3 ) +
2 / (10 ^ 4 ) +
3 / (10 ^ 5 ) + ...

which is equal to

0.0 +
0.01 +
0.001 +
0.0002 +
0.00003 +
0.000005 +
0.0000008 +
0.00000013 + ...

Fibonacci Numbers will peel the skin off your imagination:
There are unbelievable patterns woven throughout the Fib numbers!

If you examine the 'final digits' of the Fibonacci numbers, you will find strange patterns:

* Look at the final digit in each Fibonacci number:
The pattern is 60 numbers long and then it repeats the exact same sequence
over and over all the way through the Fibonacci series - to infinity.
We say the series of final digits repeats with a cycle length of 60.

* Suppose we look at the final two digits in the Fibonacci numbers.
There is a pattern here too.
After Fib(300) the last two digits repeat the same sequence again and again.
The cycle length is 300 this time.  Fib(300) means the 300th number in the Fib Series

So what about the last three digits?
and the last four digits?  and so on??

* 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
* and so on... 









			MEMORIZING PI DIGITS:
			
			To help remember these digits, people like to make up sentences or
			rhymes, called mnemonics.
			
			
			For example, "May I have a large container of coffee?'' is quite
			a famous one for the first eight digits of pi. You work out the numbers
			by counting the letters in each word.
			
			
			Here`s one for the first 31 digits of pi:
			
			
			   "Now I will a rhyme construct, 
			
			
			   By chosen words the young instruct. 
			
			
			   Cunningly devised endeavour, 
			
			
			   Con it and remember ever. 
			
			
			   Widths in circle here you see, 
			
			
			   Sketched out in strange obscurity.''