FIBONACCI: De Vina

The Fibonacci Sequence is called a “Branching Algorithm”:
an “algorithm” is simply a set of instructions to follow,
like a cake recipe: a bit of this, a bit of that, 3 parts of this and 5 parts of that…
and “branching” because each part is the sum of the previous 2 parts,
like 3+5=8 and 5+8=13…
that is why division of one Fibonacci number by its predecessor,
like 13 divided by 8
is called the “divine” proportion, a relationship of cascades,
because the word “divine” has originated from “de vina”
meaning something “of the vine”
and that something is a sacred proportion or a branching algorithm:
where the trunk is akin to a branch is akin to a twig etc
something that knows how to collect the past, adds it to the present, to create the future:
a holy trinity of sorts based on the living maths of “Natura”.

Jain 108

FIBONACCI: Floret of the Arrowhead Alpine

(Keywords:  C=8, C=13, Counter-Rotating Fields)

Nature continually surprises us with its perfected proportions.
No matter what new species of flower floret that we examine,
we can confidently predict that the counter-rotating fields
that compact and holds its precious seed, 
are in the range of Fibonacci Numbers: 

(1-1-2-3-5-8-13-21-34-55-89-144-233-377-610-987-).
Here, in this most extraordinarily beautiful Arrowhead Alpine,
we see 8 clockwise spirals and 13 Anti-clockwise spirals,
(8:13 is the same pin code for the pine cone / pine code)
Nature’s perfected mathematics,
that guarantee the optimum continuation of its species.

Jain 108

FIBONACCI ELEPHANT!

(Keywords: C=1, 2, 3, 5, 8, 13, 21, Arc, Compass, Elephant, Golden Ratio, Phi Rectangle, Phi Spiral, School, Spectrum)

I was teaching a group of young 10 years old children at a primary school in the Byron Shire, who are on the Spectrum or Special Needs class, or should I say, absolute little genius. We were constructing the Phi Golden Spiral, in the Phi Golden Rectangle. I was teaching them how to use a compass for the first time, by drawing a series of arcs that successively increased in size based on the squares: 1-1-2-3-5-8-13-21 in cms, on A4 paper, which is really the Fibonacci Sequence.
After drawing it all together correctly, I invited them to colour it in and end the class on that note. Before the bell rang, one student called it,
“Hey, I drew a Fibonacci Elephant!”

Jain 108

FIBONACCI SEQUENCE: One: The One Becomes One

(Keywords: C=1, 2, 4, 8, Binary, Cosmo-Genesis, Creation, God, Memory, Technology, Trinity, Unity Consciousness) 

We all know of the Doubling Sequence: 1-2-4-8-16-32-64 etc. It is often known as the Binary Code and is the basis of computer programming… The One becomes the Two becomes the Four is the signature for the Technological world. Very efficient for packing and storing memory.
But another interesting and more organic sequence is the Fibonacci Sequence which has a signature for the Natural or Biological world and goes like this:
1-1-2-3-5-8-13-21-34 where the next or final digit is formed by adding the two previous digits eg. 3+5=8 and 8+13=21 etc, a veritable trinity in the sense that the Past + the Present = The Future.
Notice the first pair or numbers (1,1) that begins this sequence: where “The One Becomes The One”. The “One” is Source, Creator God, and God must duplicate ItSelf to view ItSelf, to grow through the recognition of its own mirroring. The Creator needed to view its Creation so It made a copy of ItSelf to evolve through the process of Self-Reflection. I particularly love this mathematical metaphor of Cosmo-Genesis, and would be interested in any readers view on how they would interpret this mystical progression of The One Becoming The One.
Jain

FIBONACCI SEQUENCE: Wheel of 60 Pattern: Modulus 10

(Keywords: C=0, 5, 10, 60, Digital Compression, Infinity, Modulus)

”One of my favourite patterns or revelations hidden within the Fibonacci Sequence, having researched this over the last 3 decades, is the hidden 60 Pattern.
If you merely take the Fibonacci Numbers and recorded only the last digits, (which mathematically is called “Modulus 10”) a beautiful surprise emerges.
eg: in this infinite additive fib seq: 0-1-1-2-3-5-8-13-21-34-55-89-144 etc
Take the number 89 and observe that its final digit is 9.
Take the number 144 and observe that its final digit is 4.
As we continuously do this, a repetition begins at the 60^th Fibonacci number, and keeps repeating like this forever. Here are 3 of many special symmetries:
1 – All opposing pairs, passing through the centre, sum to 10
2 – The cardinal cross, like the points of North, South, East and West, are all zeroes!
3 – All the 5ives oppose one another very symmetrically forming 12 distinct spokes of the Wheel of 60.
This is again a reminder to us there exists a Greater Order amidst the apparent Chaos.

FIBONACCI DECIMAL:

The Magic of 89: The Reciprocal of the 11th Fibonacci Number

(Keywords: C=.011, 1, 11, 89, Decimal, Pattern, Reciprocal, Symmetry)

There exists an exquisite numerical pattern
inside the Fibonacci Sequence
1 – 1 – 2 – 3 – 5 – 8 – 13 – 21 – 34 – 55 – 89 – 144 –
The 11th Fib No. is 89 and when we examine its reciprocal,
that is 1/89 or 1÷89 or 1 divided by 89,
which is really the decimal expansion of the Fibonacci Sequence itself, there appears a hidden symmetry
based on the precise order of the Fibonacci Numbers.

When we add all the columns on the right hand side,
starting from the extreme right and towards the left,
and moving over any carry-overs to the left,
what appears is the decimalization of 89 being

1÷89 = .01123595505617977528089… to 23 dp (decimal places)

Jain 108