(Phi)ve and the Fibonacci Sequence

We are fractal beings of nature. We have five extremities, each having five fingers or five toes. Our heads have five openings, two nostrils, two ears, and one mouth. The essence of five creates (phi)ve. The Fibonacci Sequence. the Golden Mean, Divine Proportion, 1.618…. Ubiquitous to our existence, this ratio is the seed of life and the key to understanding how nature operates.

The Fibonacci Sequence and the golden number, Phi(and phee) are closely related to the number five. The flower of every edible fruit has five petals.  We are frugivorous by nature and the apple is the forbidden fruit. Cut one in half at its equator to reveal a pentagram of five seeds. Five is found wherever there is life, and wherever there is life there is (phi)ve.

“Man is born of the stars. With the 5 extremities from his torso and his 5 material senses, he is a living representation of the geometric symbol of the star, the pentagram. He is an ASTRONAUT, with ASTRO meaning stars and NAUT being the prefix of nautical, or pertaining to sailing or navigation. Man, as a microcosmic vessel of the most complex order and of the most ingenious design, has been cast into the ever-moving, drifting, shifting tidal seas of this universe. His body is an ark, a ship he is to command through the variant calms, storms, and high and low tides of existence. He is seafaring within an infinite cosmic ocean. It is by no mere chance that OCEAN and CANOE are anagrams for one another. Adjust your mast, point your bow North and make your journey back home.” – Claudia Pavonis

The pentagram is the symbol for excellence. Over 60 nations have stars on their flags. The square root of five is the foundation of the Golden Ratio and it is hidden in the stars, whether they are on the flag, your homework, the baseball game, or at the movie theater. We celebrate the ‘phiveness’ to reality without even knowing it.

The Fibonacci Sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144,233…

Phi = 1.6180339887…
phee= 0.6180339887…

Phi is created from this sequence found all throughout nature. Divine any number by the number before it and you will get a close approximation of Phi. The further along the sequence you go, the more accurate it becomes.

0/1 = 0
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.6666..
8/5 = 1.6
13/8 = 1.625
21/13 = 1.6153..
34/21 = 1.6190..
55/34 = 1.6176..
89/55 = 1.6181..
144/89 = 1.6179..

Phi and Phee rise above and fall below the golden rod of Phibonacci

As you can see the Fibonacci Sequence approximates Phi, creating a sine wave dipping below and then rising above the actual value

Divide each number by the one after it and you will arrive at a close approximation of phee.

1/0 = ?
1/1 = 1
1/2 = .5
2/3 = .6666..
3/5 = .6
5/8 = .625
8/13 = .6153..
13/21 = .6190..
21/34 = .6176..
34/55 = .6181..
89/55 = .6179..

The Caduceus

The caduceus is the traditional symbol of Hermes and shows two snakes wrapped around a winged staff.   The two snakes are representative of Phi and phee, as they begin at the top and approximate their value the closer you get to the bottom.

phee is the lowercase version of Phi. It has the same magical properties but is one value lower.

Phi = 1.6180339…
phee = .6180339…

The Caduceus (Phi)rals in Fibonacci’s Numbers

Interestingly 1/Phi = phee
and Phi to the power of negative one = phee
This works because Phi x phee = 1
No other set of irrational numbers allow this to happen. This is why Phi is so important and one of the reasons why mother nature decided to use it.

Further Connections:

The Fibonacci sequence is hidden in the exponentials of Phi.  I phirst saw this connection after playing around with one of Jain’s discoveries.  He showed that if you start the Fibonacci sequence with two and ten, the numbers phound in the exponents of Phi are created.

The Fibonacci series was hidden in Phi this whole time!  The first one to pop out at you, is of course, phifty phive.  If your math is rusty, an exponent is just the number multiplied by itself.  Phi to the third power is 1.6 x 1.6 x 1.6.  Phi to the negative third power would be 1 divided by (1.6 x 1.6 x 1.6).  By analyzing these exponentials, the mystery of ø reveals itself.

The Fibonacci sequence is shown in the positive exponents of Phi too, yet it decided to show its face less often.  Every other, instead of the negative exponentials.  I wish somebody would explain to me why it does this.  But perhaps this is a clue, as to how nature seeks to implode rather than explode.

Esoteric Patterns in the Fibonacci Sequence

Constructing the Universe

“It is a frequency assertion of ours that the whole universe is manifestly completed and enclosed by the Decad, and seeded by the Monad, and it gains movement thanks to the Dyad and life thanks to the Pentad. – Iamblichus

“Where plants have five fold patterns, a consideration of their souls is in place” – Johannes Kepler