The Golden Geometry of Phi

It’s important to understand where the most ubiquitous ratio in nature is found by using simple geometry.  The golden geometry of phi.  The divine proportion (the golden mean, Phi, the golden number, Fibonacci’s number) creates fractal expansion and contraction which creates life as we know it.

Earth Moon and Phi
The Golden Number = Phi = 1.6180339…

The square root of five can sound scary, but when it is visually represented it’s not as frightening.  The square root of 5 (the cross section of a double square) is essential in the formula for Phi. It’s encoded everywhere from our dna to the geometry of a nautilus shell to the milky way.  Phi is found in plants though phyllotaxis,  or the way the leaves arrange themselves around the stem.  They rotate in golden angles. 222.5 degrees is golden among the 360.

Golden Mean Phi Fibonacci
The Birth of the Golden (1+√5) / 2 = Phi

“The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.”  -D’Arcy Wentworth Thompson

golden mean fibonacci sequence divine proportion rectangle
All Life is Golden

The Circle and Square, Heaven and Earth, the transcendental and the measurable, they unite to create life.  The square roots of 2,3 and 5 have always been shrouded in mystery largely due to the fact that their decimals go on to infinity with no discernible pattern.  It was deeply disturbing to find that the cross section of a square(the square root of two)  yields an irrational number.  This probably drove Plato and pals madd!!


Five and Fibonacci Phive Phi
Phi is created from Five

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 in nature, this ratio is the seed of life for all creatures on earth and the key to understanding our reality.

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, wether 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 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 the star of five seeds. Five is found wherever there is life, and wherever there is life there is (phi)ve.

Props to Michael S. Schneider and his book “A Beginner’s Guide to Constructing the Universe”  for pointing out some of these numeric synchronicities.


Golden Mean Phi Fibonacci Earth Moon
Earth and Moon generate Phi in our units of measure

Pretend the Moon sat directly on top of Earth, and this is what you would see.  This drawing is to scale.  If a triangle is made from the center of the moon to the center of Earth, to the edge of Earth, it will be golden.  The combined polar diameters of Earth and Moon also encode Phi, using kilometers as the unit of measure.   The metric system originates from meridian measurements of Earth, so this might not be as much of a stretch as one may think.


Fibonacci Golden number phi earth moon
Earth and Moon encode Phi, no matter what unit of measure you use

The square root of Phi is 1.27019…  What this means is 1.27.. x 1.27 = Phi = 1.618…    Earth and Moon create the √ø.  I first learned this phun phact phrom Joseph Turbeville


golden mean fibonacci phi caduceus
phee Phi Pho Phum, I smell the blood of the enlightened one!

The rod is golden. Phi and phee rise above and fall below the divine proportion, getting more and more precise as the Fibonacci sequence continues on to infinity.

“In ancient Greece the advanced students of the philosopher Pythagoras who were engaged in deep studies of natural science and self-understanding were called “mathematekoi” “those who studied all.” ‘ The word ‘mathema’ signified “learning in general” and was the root of the Old English mathein,”to be aware,” and the Old German munthen, ‘to awaken.’  Today,the word math has, for most people, constricted its scope to emphasize mundane measurement and mere manipulation of quantities. We’ve unwittingly traded wide-ranging vision for narrow expertise.” -Michael S. Schneider

“Symbolism is the language of the Mysteries; in fact it is the language not only of mysticism and philosophy but of all Nature, for every law and power active in universal procedure is manifested to the limited sense perceptions of man through the medium of symbol.” -Manly P. Hall

Esoteric Patterns in Fibonacci

Fibonacci Sequence

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