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Understanding the Fibonacci Sequence and Golden Ratio

Fibonacci sequence in a sunflower

The Fibonacci Sequencegolden-ratio-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 seen from a Chambered Nautilus to a Spiraling Galaxy

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
Sunflowers have a Golden Spiral seed arrangement. This provides a biological advantage because it maximizes the number of seeds that can be packed into a seed head.

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.

(A beautiful short film on Fibonacci sequence in Nature – ‘Nature by Numbers’)

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)

Image source

Phi Golden Ratio

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FALLEN SOLDIER The tyrannical tentacle of the state has caught one of our own. Gary Z McGee is in jail for the petty offense of not pulling over quickly enough. He is now charged with two felonies: Evading arrest and endangering a child, because his son was in the RV. The license plate was stolen from his vehicle during his trip back home from visiting his family over the holidays, and he was being pulled over for speeding and driving without plates. He is currently awaiting his day in court and will be sending us his words, as he is able. Living in the most incarcerated country in the world Gary Z McGee is just the latest victim of the prison industrial complex. He faces 2 to 15 years in prison if convicted. Please feel free to send him words of your own to P.O. BOX 39 Sierra Blanca, Texas 7985. As is usual in this system, people with money can bail themselves out and afford proper legal counsel. Unfortunately Gary is not in this category. His bail amounts to $8,500.00. And the minimum to obtain legal counsel is $1,600.00. Any donation is greatly appreciated. To send a care package: My care or 866-643-9557. To put money on his books 866-394-0490. Facility code #5500 booking number 2016016069. If you would like to donate to his bail or defense fund we have set up a pay pal account for
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    Gemini from the United States, believes in Existentialism, Transhumanism and PLUR. Lives to protect the truth and make the world better.

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