__What if we divide the numbers of the Fibonacci Series by NINE?__4181/9 = 464.55555*rpt

2584/9 = 287.11111*

1597/9 = 177.44444*

..........

34/9 = 3.77777*

21/9 = 2.33333*

13/9 = 1.44444*

__A Pattern emerges esp from the last three:-__

**Fn / 9 = F(n + 5) / 100 plus "extra"...eg .004444* or .003333***

F14 is 377, divide by 9 = 41.88888*

F14 + 5 = F19 = 4181; F19 / 100 = 41.81000- extra is .0788888*

F13 is 233, divide by 9 = 25.88888*

F13 + 5 = F18 = 2584; F18 / 100 = 25.84 plus .04888*

.07888 / .04888 = 1.6137479

Higher number ratios of "extras" = closer to 1.618, the "Golden Mean"

eg F19/9 = 464.555*. F24/100 = 463.68; difference is 0.87555*

F18/9 = 287.111*. F23/100 = 286.57; difference is 0.54111I

ratio of differences is

**1.618069**

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One can compile tables of the Fibonacci numbers divided by 9; also by 2, 3, 4, 5, 6, 7, 8.

**Only one number to F25 divides evenly by all single digits except for 5.**

ie number F24 which is 46 368

ie number F24 which is 46 368

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__What if we multiply the first 25 Fibonacci Numbers by NINE?__I shall only do a few:-

17711 x 9 = 159 399

10946 x 9 = 98 514

6765 x 9 = 60 885

4181 x 9 = 37 629

2584 x 9 = 14 373

987 x 9 = 8 883

610 x 9 = 5 490

377 x 9 = 3 393

233 x 9 = 2 097

144 x 9 = 1 296

89 x 9 = 801

55 x 9 = 495

**An Equation emerges:- 9 x Fn = 1/2F(n+6) + 1/2F(n-6) !**

eg. 987 x 9 = 1/2 x 17711 + 1/2 x 55

=8855.5 + 27.5 = 8 883 = 987 x 9 !

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**,**

__Multiply by 18__**then the Equation is 18 x Fn = F(n+6) + F(n-6)**

eg. 4181 x 18 = 75258 = 75025 + 233 !

Try it for other numbers, even huge ones.....

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__Multiply by 27,__then

**the Equation is 27 x Fn = 10 x F(n+2) + 1/2F(n+1) + 1/2F(n-8)**

eg. 27 x 10946 = 10 x 28657 + 1/2 x 17711 + 1/2 x 233

.........................= 286570 + 8855.5 + 116.5 = 295542

.........................= 27 x 10946 !

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__Multiply by 36, (4 x 9).__The

**Equations might be 36 x Fn = 100F(n-3) + 10 x Fn + F(n+1) + F(n-2) + F(n-4) + F(n-9).....OR**......

**36 x Fn = 100Fn-3) + 10F(n-3) + F(n+4) + F(n+2) + F(n-1) + F(n-4) + F(n-6) + F(n-10) - F(n-12)**

try 233 or 610; I will check on this sometime.....

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__What if we Multiply by 45, (5 x 9), ?__**The Equations are:-**

**45 x Fn = F(n+8) - F(n+1) - F(n-3) - F(n-5) - F(n-7)......and.....**

**45 x Fn = F(n+7) + F(n+5) + F(n+3) + F(n-1) + F(n-8)......then.....**

**F(n+8) - F(n-8) = F(n+7) + F(n+5) + F(n+3) + F(n+1) + F(n-1) + F(n-3) + F(n-5) + F(n-7) !**

try 610.....

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Something might happen with x54, x63, x72, x81, etc; I have not tried it yet...

What use is it? It is just a buzz to see Patterns, " palindromes" almost!

There might be a particular model which one can make with these patterns.....

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__What if we multiply by 19?__**An Equation that emerges is:-**

**19 x Fn = F(n+6) + Fn + F(n_6) !**

eg. 19 x 610 = 11 590 = 10946 + 610 + 34, correct.

Try other numbers; see how far up the series one can go with this!

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__What if we multiply by 29?__**The Equation is 29 x Fn = F(n+7) - F(n-7) !**

eg. 29 x F18 = F25 - F11

......29 x 2584 = 74936 = 75025 - 89, = correct.

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__Multiply by 39:-__**Equation seems to be 39 x Fn = 1/2 F(n+9) + Fn - 1/2 F(n-9) !**

eg. 39 x 610 = 46368/2 + 610 - 8/4

.....................=23184 + 610 - 4 = 23790. = correct.

eg. 39 x 144 = 10946/2 +144 - 2/2

.....................=5473 + 144 - 1 = 5616, = correct.

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Multiply by 59 or 99:-

there could well be Patterns; I am working on it.....

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At least I have got it all down on paper and online

There could well be corrections to any mistakes...

At least it satisfies my curiosity.

__What does the number nine signify indeed?!__

__For the Maya, the number nine was to be worshipped.__Nine "Lords of the Night" were painted on the tomb walls of the Temple of Inscriptions.

1/9 = 0.1111*rpt

2/9 = 0.2222

3/9 = 0.3333

....

8/9 = 0.8888

....

10/9 = 1.1111

**20/9 = 2.2222rpt**

nine based decimal system is half as complex as today's 10 based system,

This is from

**page 324 of " The Mayan Prophecies"**

__by Adrian G. Gilbert and Maurice M Cotterell publ 1995 Element Books, Inc.__

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__You might like to play with the first 135 Fibonacci numbers:-__

__See post 5/4/2013__

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