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Understanding the Fibonacci Sequence and Golden Ratio

The Fibonacci Sequence

The Fibonacci sequence is possibly the most simple recurrence relation occurring in nature. It is 0,1,1,2,3,5,8,13,21,34,55,89, 144… each number equals the sum of the two numbers before it, and the difference of the two numbers succeeding it. It is an infinite sequence which goes on forever as it develops.

The Golden Ratio/Divine Ratio or Golden Mean -

The quotient of any Fibonacci number and it’s predecessor approaches Phi, represented as ϕ (1.618), the Golden ratio. The Golden Ratio is best understood geometrically by the golden rectangle. A rectangle unevenly divided resulting into one square and one rectangle, the square’s sides would have the ratio of 1:1, and the new rectangle would be exactly proportionate to the original rectangle – 1:1.618.

This iteration can continue both ways, infinitely. If you plot a quarter circle inside each of the squares as they reiterate, the golden spiral is formed. The golden spiral is possibly the most simple mathematic pattern that occurs in nature like shells of snails, sea shells, horns, flowers, plants. Numbers are only what we use to organize quantitative information.

golden ratio spiral galaxies

The Golden Ratio can be applied to any number of geometric forms including circles, triangles, pyramids, prisms, and polygons. The golden ratio is formed by thirds within thirds, sixths, the connection between two and three, including every even and odd number itself. The ratio itself represents the transcendence of numbers, understanding our world is not numbers, but what numbers represent. Through the spiral, the ratio illustrates how the numbers, all quantities, are quality. Eventually, all quality can be represented through quantity. Properties qualitative and quantitative are just labels of information, our gathered indisputable fact.

Fibonacci sequence in a sunflower

If you graph any number system, eventually patterns appear. In mathematics, numbers and their patterns do not only continue infinitely linear, but in all directions. For example, considering infinite decimal expansion, even the shortest segments have an infinite amount of points.

Our universe and the numbers not only go on infinitely linear, but even it’s short segments have infinite points.

The golden ratio is not the only mathematical pattern that reaches infinity, there are many other patterns as well that reach infinity. Knowing this, ask yourself, how could infinity occur twice? If something were to happen infinitely, how could it happen twice? The answer is simple, infinity represents what is eternal, what is truly whole. For example, if infinity were to be used as a variable in mathematics like all other numbers, it would be denoted as 1∞, 2∞, 3∞, 4∞, etc.

The oneness of everything factual is what you know, what you perceive, what you are aware of, is all the universe looking at itself. This is the universe, even you are the universe, us and everything we know is all the same thing.

Since the numbers are everywhere, everything is a part of a pattern. Reflections of reflections, wheels within wheels. Life itself is a Fractal. (Another video on the Egyptian ‘Temple of Man’ is a symbolic representation of the Fibonacci series of balanced organic expansion and an expression of the underlying principles of life in the universe)

Thanks to Fractal Enlightenment!

http://www.spiritscienceandmetaphysics.com/understanding-the-fibonacci-sequence-and-golden-ratio/

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Tags: Fibonacci-Sequence, Golden-Ratio-Divine-Ratio

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Comment by Avatar on June 3, 2014 at 2:19am

So true, Hellen...glad you enjoyed the video...it's all so fascinating.

Comment by hellen on June 3, 2014 at 1:19am

...balance through growth,change and expansion ...great video Avator ..i also study Drunvalo Melechizeke's Sacred Geometry ..we are a living temple ...divine blue print ..

Comment by Avatar on June 1, 2014 at 3:56pm

I love this subject too, Stick...I find it utterly fascinating. Thank you for mentioning the Drunvalo Melchizedek books...the more that sheds light on our origins the better for all of us. We need to open our eyes and see what's truly right in front of them. ;)

Comment by Stick on June 1, 2014 at 7:46am

~Love this subject, Avatar... thanks for posting. I've studied with Drunvalo Melchizedek & consider his 'Flower of Life' books to be a great entry point for those wishing to 'remember' more about their true origins. Sacred Geometry is a profound gateway to deepening our understanding of this experience we call, Life. Seek & you shall find, Ashtar Massive ;-) ~InLight555

  

( ( ( It's ALL Happening Right Now!!! ) ) )

 

Comment by Avatar on May 31, 2014 at 10:10pm

Thank you for sharing this info, Drekx and I wish you would do it more often and even though I'm sure you have in the past we are gaining new members everyday who need to be made aware of this valuable and important information. You have so much to offer that's of value to us.

I am a great respecter of P'taah who is very loving and cares deeply for humans...what a great inspiration he is for me and many others. I once asked him for a sign in the night sky and he provided it which humbled and encouraged me to know he was listening and there for me.

It's sad what 'they've' done to keep these beneficial devices from us but it will not always be this way and one day soon the earth will be changed for the better.

Comment by Drekx Omega on May 31, 2014 at 7:50pm

Thanks Avatar.....It always brings tears of joy to my eyes when I can at the very least, inspire and assist my fellows...You will always find me a great advocate for aetheric energy, as I have been so honoured to be taught in it's application myself....It is a humbling science, which is so amazingly different to what we know as commonplace technology.......It feels right when I am permitted to utilise such devices, in service to the divine plan....In the 1970s, the Plejaren Federation attempted to present aetheric energy devices for public scrutiny, via their genuine contactee, Billy Meier.....Unfortunately, friend Billy and his beloved family, became targets for assassination, by the cabal and their agents.....thus, henceforth, our Plejaren collegues have advised the Sirians (who aquired the responsibility for earth from Ptaah) to only allow the loan of such special devices....As to keep an aetheric energy device at home, or at a business location, can lead to a black ops raid....or execution of Ground Crew/contactees....

I will provide a link, which illuminatingly describes some of our rew work.....But from the perspectives of those who are not fully aware of what our GFL ground crew purpose is....They describe it as political and mysterious....maybe it is, to some degree...  ;-) But I'll share it with anyone who opens their minds to aetheric energy tech applications....which is the future science of earth....and the only science.

Kind regards, Drekx

http://www.enterprisemission.com/Norway-Message3.htm

Comment by Avatar on May 31, 2014 at 7:25pm

Unfortunately, Thori many of us have had unsatisfying relationships. I never until just recently thought of my twin flame but now do...I'm so happy for those who find theirs. I agree it's always best to take a step back and re-evaluate our relationships and try to figure out what has gone wrong and what we need to do to make them work. It takes a while for many of us to figure out who or what we really want in this life...it's often better to get to know ourselves first but it's not until we're older that we figure that out.

Nice getting to know you, Thori...<3

Comment by Avatar on May 31, 2014 at 7:14pm

Very interesting, Drekx. I agree that any advancement that would allow us more efficient energy and of course, healing modalities would be confiscated...the dark cannot allow that. However, I have complete faith that one day soon that will all change.

Great comment, Drekx...thanks!

Comment by Avatar on May 31, 2014 at 7:09pm

Sounds very romantic, Feather. ;) My guy was a whiz in math and since I'm not much for math I was very impressed. LOL

Comment by Drekx Omega on May 31, 2014 at 6:56pm

Actually I'm always very happy when you guys bring up the Fibonacci series, the golden mean phi, divine proportion and sacred harmonics.......This is the very portal that connects the dense physical plane with the higher aethers.....It actually enables us to use a higher science, which is in effect based upon the LIFE FORCE itself....Namely, VRIL, ORGONE, PRANA.....I usually describe this simply as aetheric energy.....and it is the polar opposite of the current combustion tech, we see everywhere on surface earth at present...

I would like to state, that aetheric energy devices are currently prohibited by the dark cabal and if any individual were to possess such a device, usually through scientific investigations and re-discoveries made, then they would not be permitted a patent, and their notes would automatically be confiscated under "national security" laws...

 

However, the GFL do possess aetheric energy devices and do loan them out to GFL Ground Crew for specific purposes only....They are not permitted to be retained by said crew, because it would be a threat to us and also our familes...

YET, we can be taught the principles and operational applications of this tech and it is superb...It is based on the sacred harmonics of nature and links electro-magnetism with GRAVITY.....

As a means for propulsion and numerous other effective applications.....It is SAFE & CLEAN, as it is not entropic....at is based upon life force, so is the polar opposite of entropic decay....

You could call it a polar opposite in scientific principles.....

Radiation and combustion inherent in the science of today, furnish us with such applications as the nuclear reactor, the rocket/missile, the internal combustion engine and many others....

This is the science of entropy...decay, friction, centrigugal, destruction and degradation.....We do see it in the universe, when stars decay.......The energy which sustains stellar, planetary and human life, is actually hidden from the scientific model known......

It is the life principle and based upon the harmonic centripetal spiral...which evades friction and offers the line of least resistance in motion...

 

I will encourage all to study the works of Viktor Schauberger...an Austrian scientist who re-discovered this principle, among several others...

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