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Golden Ratio Media, LLC is a Multimedia, Production and Website firm located in the Flathead Valley, Kalispell

Golden Ratio Media is Located in Kalispell, Montana

Golden Ratio Media, LLC was formed in 2008 as a web design and video production company. As a Christian company, we see a higher order and purpose in everything we do, and chose to believe there is a grand purpose and intelligence behind every person, product, brand or company we work with. We promise to give our highest standard in quality and commitment to you and your business. We service clients all over the nation but are proud to be located in Kalispell, Montana.  We are a one-stop shop for all of you multimedia, production and website hosting needs

Journey Down the Golden Spiral

Our history of the Golden ratio goes back a few thousand years. Leonardo Da Vinci, Plato, Euclid, Roger Penrose, and Johannes Kepler all dabbled with it in the context of their work. But the divine proportion and its mystery extends well beyond the finite workings of the human mind, and in essence is the proportional make up of the natural world we find all around us. As some people have put it, this is the “fingerprint of God.”

Take a moment and explore the marvelous ratio that has had the brightest minds across the ages of human kind marveling at its intricacies.



In Math

Golden Ratio = 1.61803398749895...

The essence of the Golden ratio is based off of the Fibonacci sequence:

This sequence is derived by adding the previous number to the proceeding number,
0+1 = 1, 1+1 = 2, 1+2 = 3, 2+3 = 5, 3+5 = 8, 5+8 = 13, etc...

By taking two numbers in the sequence and placing them 1 over the other for example, 21/34 = .617 you get very close to the .618033987 of the Golden Ratio and it gets closer the larger the numbers get.

The Golden Ratio has many complex mathematical expressions, but the simplicity in which it can be represented as shown in the figures below are what makes this particular mathematical function so elegant and appealing and is why so many of the worlds most brilliant minds have dedicated themselves to probing its mystery. We find it in almost everything we look at, a true blueprint for the created order.

Greek Letter Phi, used to represent the Golden Ratio
as a mathematical expression.

The Golden Section is a ratio or proportion defined by
the number Phi ( = 1.618033988749895... )

The Golden Rectangle shows how the Golden Segment can be used to partition a rectangle into a square, which can in turn be partitioned into another square and so on.

The Golden Spiral is derived by connecting opposing corners with a expanding curve that also reflects the 1.618033988749895... ratio.



In Art

Whether by accident or purposeful the Golden Ratio is found in architecture, paintings, sculptures and even music. An impressive array of infinite uniformity is all around us, and human kind has intuitively cued into this harmony through the arts as our own way of reflecting and resonating with the divine.

In the painting the Last Supper, by the artist Salvador Dali'
we find the Golden Ratio used.

Euclid 325-265 B.C. is traditionally credited with describing the Golden Ratio but, the Parthenon which was created in 490–430 B.C. shows the ratio throughout its construction.

Music intervals are all based on the Golden Ratio and the Fibonacci sequence. As expressed in Paul Hindemith's The Harmony of Worlds based on Johannes Kepler's work.

A sculpture called the Ratio by Andrew Rogers in Jerusalem is arranged into boxes that grow proportionally larger according to the Fibonacci sequence.



In Nature

Is our ability to recognize and mimic the Golden Ratio in creation just a convenient way for the human mind to organize and define beauty in what we see in the world? Or is it exactly how our progenitors conceived it, as something scared, a seal placed there deliberately as a signature on a piece of artwork by a truly extraordinary being?

Joints in the human body or any skeletal system all
incrementally decrease per the Golden Segment tapering
off in a subtle natural way.

Galaxies and planet formations exhibit the Golden ratio.
Look no farther than our own solar system and its
planetary orbits and you find it there.

Flowers and sea shells are some of the most common examples of the Golden spiral in nature. The ordered and methodical arrangement is very appealing to our human eyes.

The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.34 and 21, are numbers in the Fibonacci series.



In History

Born: 569 B.C.
Apprentice to: Pherecydes

The Greek philosopher Pythagoras discovered the Golden Proportion by listening to blacksmith’s hammers hitting their anvils and the sounds given off. He noted that the size and shape of the sound produced varied accordingly with the size and thickness of the piece of metal being struck. Through this observation he was able to determine a pattern of tones that would repeat itself in  ever-increasing increments up or down the scale.

He went to great lengths to keep this finding a secret, and was awed and fascinated with implications of such harmonious mathematics playing out in creation. He admonished his pupils to never reveal its mysteries or they would face the punishment of death. The symbol of the Pythagorean brotherhood was the pentagram, in itself embodying several Golden Means.

The entire design of the Parthenon and many works of classical architecture that sprang up during this time, had the Golden Ratio infused into every aspect of their structures. This was a true indication of the reverence the ancient Greeks placed into this remarkable sequence of numbers.



Leonardo Da Vinci
Born: April 15, 1452
Apprenticed to: Andrea di Cione 1466-1476

Though Leonardo wasn't particularly skilled in mathematics, his work in art, engineering and anatomy showed he was very well aware of the Golden Ratio. His prolific detailed drawings and sketches were filled with excellent examples of how the natural world exhibited patterns and even incorporated the Golden Rectangle in many of his most famously recognized paintings.

In the 1490s Da Vinci under the tutelage of Luca Pacicoli studied mathematics and prepared a series of drawings of regular solids for Pacioli's book De Divina Proportione, published in 1509. This book is an incredible treatise on the Golden Ratio and inspired generations of scholars, and artisans to look at the Golden Ratio and incorporate it into their own body of work.







Johanness Kepler
Born: January 6,1572
University: Tübingen University (1587)

The first two 'Laws of Planetary Motion' were described by Kepler in 1609 in his brilliant book called Astronomia Nova ('the new astronomy'), showing the planets as elliptical rather than  circlular, making a staggering leap from traditionally recognized astronomy. In this work he showed through mathematical proofs developed from the Golden mean and Fibonacci sequence how a planet's speed is not uniform but varies at different stages of its orbit. The 'Third Law' which describes the relationship of the Sun and the time it takes to complete an orbit by the planetary spheres, was announced in Harmonice Mundi ('harmony of the world'), published 1618. The laws provided the framework for Isaac Newton in the end of the 17th century to conceptualize his universal gravitation theory thus changing the way in which we perceive the harmony of planetary motion.

In his book called the Harmony of the World, Kepler uses the platonic solids to describe the planetary orbits. This is represented in a model that has a complex arrangement of the five platonic solids in a repeating fashion, one inside of the other. These five platonic solids are called the tetrahedron, cube, octahedron, dodecahedron, icosahedron, and are shown in Kepler's model each corresponding to a particular planetary orbit.





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