Fibonacci: Forgotten Numbering System

 

Golden Ratio & Golden Section

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller.

Expressed algebraically:

The golden ratio is often denoted by the Greek letter phi (Φ or φ).
The figure of a golden section illustrates the geometric relationship that defines this constant. The golden ratio is an irrational mathematical constant, approximately 1.6180339887.

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Golden Rectangle

A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1: j (one-to-phi),
that is, 1 :  or approximately 1:1.618.

A golden rectangle can be constructed with only straightedge and compass by this technique: Construct a simple square Draw a line from the midpoint of one side of the square to an opposite corner Use that line as the radius to draw an arc that defines the height of the rectangle Complete the golden rectangle

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Golden Spiral

In geometry, a golden spiral is a logarithmic spiral whose growth factor b is related to j, the golden ratio. Specifically, a golden spiral gets wider (or further from its origin) by a factor of jfor every quarter turn it makes.

Successive points dividing a golden rectangle into squares lie on
a logarithmic spiral which is sometimes known as the golden spiral.
Image Source: http://mathworld.wolfram.com/GoldenRatio.html

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Golden Ratio in Architecture and Art

Many  architects and artists have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. [Source:Wikipedia.org]

Here are few examples:

Parthenon, Acropolis, Athens.
 This ancient temple fits almost precisely into a golden rectangle.
Source: http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm

The Vetruvian Man"(The Man in Action)" by Leonardo Da Vinci
We can draw many lines of the rectangles into this figure.
Then, there are three distinct sets of Golden Rectangles:
Each one set for the head area, the torso, and the legs.
Image Source >>

Leonardo's Vetruvian Man is sometimes confused with principles of  "golden rectangle", however that is not the case. The construction of Vetruvian Man is based on drawing a circle with its diameter equal to diagonal of the square, moving it up so it would touch the base of the square and drawing the final circle between the base of the square and the mid-point between square's center and center of the moved circle:

Detailed explanation about  geometrical construction of the Vitruvian Man by Leonardo da Vinci >> 
 

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Golden Ratio in Nature

Adolf Zeising, whose main interests were mathematics and philosophy, found the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors. In these phenomena he saw the golden ratio operating as a universal law.[38] Zeising wrote in 1854:

The Golden Ratio is a universal law in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form.

Examples:

Click on the picture for animation showing more examples of golden ratio.
Source: http://www.xgoldensection.com/xgoldensection.html

Source: http://www.goldennumber.net/hand.htm

A slice through a Nautilus shell reveals
golden spiral construction principle.

The Piri Reis Map

If you try and search the Internet using "Piri Reis Map" as keywords, you will come across many websites dedicated to "mysteries", which allege that this map, dated "Year 919 in Muslim Calender", contains a precise representation of the coasts of Antarctica, a continent unknown at that time. According to Charles Hapgood, author of "Maps of the Ancient Sea King: Evidence of Advanced Civilization in the Ice Age", those maps contain a precise representation of Antarctica as it was before last ice age.

According to many mystery enthusiasts, the map was either based on ancient representations, perhaps dating as far as the mythical Atlantis, or were drawn from pictures taken from sky. That because the knowledge available as of 16th century cannot explain such stunning correspondence with reality.

Both Hapgood and Hancock claim that the representation of the Antarctic continent is incredibly precise. And since it clearly indicates rivers, lakes and mountains, this ancient cartographic model could date as back as 15,000 years ago. They also suggest that the map was drawn basing on surveys, which must have been taken from a satellite in a geostationary orbit over Egypt.

What is known today as the map of Turkish admiral Piri Reis is actually just a fragment of the original, much larger map, which represented the whole known world. This surviving represents Atlantic Ocean, western coasts of Europe and Africa, and eastern coasts of America. It is dated "Muslim Year 919". According to its author, the map was compiled from "twenty older charts and eight planispheres". It is very likely that Reis also examined the journey accounts written by early explorers of Hasan Fehmi and publishes by Yusuf Akcura, President of the Society for Turkish Historical Research, in 1935 in his work "Piri Reis Haritasi", and then re-published by Ayse Afitinan in "The oldest map of America" in 1954. It is worth nothing that, although this and other maps abound with clear and perfectly readable text and captions, the authors who present them as proof of their extravagant these quotes nothing but few lines. Yhe only region of South America to look sufficiently detailed on the map is the coast of Brazil, although the river of Amazon is drwan twice, in different locations.

Piri Reis himself states, in a note, that he consulted the charts of Christopher Columbus. The peculiar configuration of the Caribbean area in his map seem to confirm that statement. That region of the American continent is indeed improperly represented: it features a large island arranged north-south which cannot be identified with Cuba, not even by rotating the whole map counterclockwise by 90 degrees.

But what mystery lovers are most enthusiast about is the bottom edge of the map, which is said to represent Antarctica. Some claim that Land of Queen Maud and other features Antarctica are clearly recognizable on the map, even though that continent was not explored but many centuries later. Unfortunately these people, including Hancock, claim the hypothesis without making any cartographic comparison or first-hand check: they just accept Charles Hapgood's statements as true.

The Stone Spheres of Costa Rica

Intro

One of the strangest mysteries in archaeology was discovered in the Diquis Delta of Costa Rica. Since the 1930s, hundreds of stone balls have been documented, ranging in size from a few centimeters to over two meters in diameter. Some weigh 16 tons. Almost all of them are made of granodiorite, a hard, ingenous stone. These objects are monolithic sculptures made by human hands.

The spheres number over 300. The large ones weigh many tons. Today, they decorate official buildings such as the Asamblea Legislativa, hospitals, and schools. You can find them in museums. The spheres were previously unknown to the inhabitants and they could offer no explanation of who made them or how old they were. Plantation workers bulldozed them and largely ignored them until rumors started spreading that they may contain gold or precious jewels. Many balls were drilled or cracked open with dynamite, only to reveal that they were composed of soil rock.

When news of these rock balls reached the authorities, several whole specimens and parts of the fractured balls were taken to the National Museum in San Jose. Here, they attracted the attention of Doris Stone, daughter of a United Fruit executive, who photographed them and wrote an article about the phenomenon in the 1943 edition of American Antiquity.

Since then, archaeologists have been perplexed by the stones. Thousands have now been found. Some are as small as four inches -- while others are as massive as eight feet in diameter. Estimates of their age goes back some 1,600 years, yet no one can be sure how they were made, by who or why.

Myths

The spherical stones certainly took a long time to make. The age of these stones place them at a time when no iron tools were known to exist in that region, meaning the spheres were somehow formed by stone implements. Yet no stone tools of this era and geographic are have been found.

All of this has lead some researchers to speculate that the stone spheres were made by some advanced civilization.

Some local legends tell of a magic potion that was able to make the rock soften and hence easily manipulated. This same legend persists to explain other phenomenon such as the precisely carved and fitted stones of Machu Pichu. One legend says that the spheres were formed around a coffee bean or nuggets of gold.

Other legends claim that the spheres were part of a game, once played by giants that inhabited the Earth or that the spheres represent stars of constellations in the sky.

Many of the spheres are made of granite like rock. The closest granite quarries of similar rock are in the Talamanca Mountain some 50 miles away. Although the stones could have been transported down the nearby Terraba River, no unfinished stones or evidence of excavation in the mountains has ever been found.

The construction of the spheres would have required a high degree of measurement and mathematics. One perplexing question is why this same level of skill and precision has not been found in any other artifacts of this region or era.

Georgia Guidestones: A modern Stonehenge

On one of the highest hilltops in Elbert County, Georgia stands a huge granite monument. Engraved in eight different languages on the four giant stones that supports the common capstone are 10 Guides, or commandments. That monument is alternatively referred to as The Georgia Guidestones, or the American Stonehenge. Though relatively unknown to most people, it is an important link to the Occult Hierarchy that dominates the world in which we live.

The origin of that strange monument is shrouded in mystery because no one knows the true identity of the man, or men, who commissioned its construction. All that is known for certain is that June 1979, a well-dressed, articulate stranger visited the office of the Elberton Granite Finishing Company and announced that he wanted to build an edifice to transit a message to mankind. He identified himself as R.C Christian, but it soon became apparent that was not his real name. He said that he represented a group of men who wanted to offer direction to humanity, but to date, almost two decades later, no one knows who R.C Christian really was, or the names of those represented. Several things are apparent. The messages engraved on the Georgia Guidestones deal with four major fields:

1. Governance and Establishment of a world government.
2. Population and reproduction control.
3. The environment and man's relationship to nature.
4. Spirituality.

The languages on the stone are:
-  Spanish
- English
- Russian
- Chinese
- Arabic
- Hebrew
- Swahili
- Hindi

The old languages are:
- Egyptian Hieroglyphics
- Sanskrit
- Classical Greek
- Babylonian Cuneiform

Here are the messages written on the monument

1. Maintain humanity under 500,000,000 in perpetual balance with nature.
2. Guide reproduction wisely - improving fitness and diversity.
3. Unite humanity with a living new language.
4. Rule passion-faith-tradition-and all things with tempered reason.
5. Protect people and nations with fair laws and just courts.
6. Let all nations rule internally resolving external disputes in a world court.
7. Avoid petty laws and useless officials.
8. Balance personal rights with social duties.
9. Prize truth-beauty-love-seeking harmony with the infinite.
10. Be not a cancer on the Earth - Leave room for nature - Leave room for nature.

The parallel stories of wiping out Earth's 'Unwanted' population has always been coming up in various religious stories. Let's say, in Bible, the story of Noah and his Ark. In Hindus, how Vishnu after every 'Yuga' reincarnates or his various 'Avatars' help wipe out the filths of the Earth; his next Avatar's due at the end of 'Kali Yuga' - the present 21st century named 'Kalki', the previous one was 'Krishna'. So, were the maker's of the guidestone knowing the prophecy of the upcoming apocalypse?

The message of the American Stonhenge also foreshadowed the current drive for Sustainable Development. To this day, many account this message with the Nazism ideology of "Space Lebensraum". That's why many times, the social activists and the grave diggers have tried to hinder the monumental space with various graffitis.

Yoko Ono, the widow of John Lenon, was recently quoted as referring to the guidestones, saying:
I want people to know about the stones.... we're headed toward a world where we might blow ourselves up and maybe the globe will not exist....it's a nice time to reaffirm ourselves, knowing all the beautiful things that are in this country and the Georgia Stones symbolize that."

The group that made the guidestones - unknown - is one of the many groups working together toward a New World Order, a new world economic system, and a new world spirituality. Behind those groups, however, are dark spiritual forces. Without understanding the nature of those dark forces it is impossible to understand the unfolding of world events.

Who is R.C Christian? 

 The official story offers a number of facts about the Chrisitan figure. There are quotations supposedly from the man himself along with the comments from Joe H. Fendley, Sr. and Wyatt C. Martin - the only people who have met R.C Christian, while Martin is the only person who knows for sure his identity. Christian apparently stated, "I only use that name because I am a follower of the teachings of Jesus Christ." Apart from his religious belief, Christian is described as having served in the WW II and described himself as patriotic American in every sense of the world. Obviously a man of great wealth, he also "appears to be well traveled and intelligent man" who travelled in Europe and was impressed with various historcial monument like the stonehenge.

In Randall Sullivan's well-circulated article on the Georgia Guidestones for Wired, it is revealed that Christian kept in regular contact with Martin: regular letters and occasional meetings in Athens. The last point of contact was close to the events of 9/11 and Martin assumes, based on age, that Christian might now be deceased. In their meetings, Christian never discussed the books and the well kept cotact with the only person that knows his identity indicates a desire to perform the role of Christian to the only person for whom he could.