A Theoretical Fibonacci Christmas Tree

*click to enlarge diagram. "back" to return.
Wishing you all a very happy christmas and a bright New Year in 2011.

Love is the strongest Power in the universe.
Some of us feel so traumatised and distressed at times that it feels a most difficult thing to love anyone or anything. At least we can try; practise the Form, and the reality may follow. The Dalai Lama is our shining example. Especially the most troublesome people need love, for that is ultimately the only remedy for our human tragedies. Peace on Earth and Goodwill to all men and women and children and Sentient beings and even to non sentient beings. Alleluja.


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27/12/2014  Thank you to all the people who visit this here Page at Christmas Time over the years.  This year there is a crocheted Cone like a Tree and more interesting information.  Happy 2015 to ALL.

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More series, and IFF, if and only if....

*please note: these tables begin with F(n) : F1 is 0, F2 is 1, F3 is 1, F2 is 2, etc. Most other websites begin with F0 is 0, F1 is 1, F2 is 2 etc. Therefore my calculations are one out.
Please note
There is an error in addition in F81. It should be 23 416 728 348 467 685
and also in F99. It should be 135 301 852 344 706 746 049.
All the nearby numbers need correction also.



What is signifant about 192?

Here is the equation:- F(n) x 192/100000 = F(n-13) metres
which is the length of each row or edge iff 1000 stitches measure 192 cm.



I have begun an ambitious model, F21 = 6765, already completed, for a seashell, next row will be 10946 stitches, if I can bear to finish it.
I wondered how long is this edge, so I measured 1000 stitches and it was about 208cm.
192 cm is very close to 208.

More next time, my time on library computer is up.

Fibonacci Series

*** please note: Most websites begin with F0 = 0, F1 = 1, F2 = 1, F3 = 2, F4 = 3 etc.
*** my F1 is 0, F2 is 1 etc. Thus all my data is one iteration different. Here are some more ratios:-


F(n-1)/F(n)
F11/F12 = 55/89 = 0.6179775
F16/F17 = 610/987 = 0.6180344
F17/F18 = 987/1597 = 0.618338
F29/F30 = 317811/514229 = 0.6180339

F(n-2)/F(n)
F10/F12 = 34/89 = 0.3820224
F16/F18 = 610/1597 = 0.3819661
F20/F22 = 4181/10046 = 0.381966
F31/F33 = 832040/2178309 = 0.381966

F(n-3)/F(n)
F10/F13 = 34/144 = 0.236
F15/F18 = 377/1597 = 0.2360676
F19/F22 = 2584/10946 = 0.2360679
F30/F33 = 514229/2178309 = 0.2360679

F(n-4)/F(n)
F10/F14 = 34/233 = 0.1459227
F14/F18 = 233/1598 = 0.1458985
F18/F22 = 1597/10946 = 0.145898
F29/F33 = 317811/2178309 = 1.45898

F(n-9)/Fn)
F10/F19 = 34/2584 = 0.01315
F29/F38 = 317811/24157817 = 0.0131556
F30/F39 = 514229/39088169 = 0.0131556

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There is an excellent website http://www.evolutionoftruth.com/
which gives us many more relationship numbers regarding phi.
5/3 = 1.66 = phi
8/5 = 1.6
eg phi squared = phi + 1.
1/phi = phi-1 ie 0.61804
1 squared + 1 squared + .... F(n) squared = F(n) = F(n+1)
34/21=1.6190476
Relationships with DNA and Solar System
http://www.goldennumber.net/

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F(n-13) x 100000/F(n) F10
F10 x 100000/ F23 = 3400000/17711 = 191.97109
F15 x 100000/F28 = 37700000/196418 = 191.9376
F20 x 100000/F33 = 418100000/2178309 = 191.93787
F24 x 100000/F37 = 2865700000/14930352 = 28657/149.30352 = 191.93787
F30 x 10000/F43 = 51422900000/267914296 = 514229/2679.14296 = 191.93787
F30 x 100000/F43 = 51422900000/267914296 = 514229/2679.14296 = 191.93787

All the way here, it is close to 192.
What does this signify?
A brand new equation!