Golden section

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Golden Section

The Golden Section in Ancient Egypt

Ancient Egypt is perhaps the most facinating of the ancient civilizations. Even the Ancient Greeks thought themselves to be a young and inexperienced society compared to the Egyptians. Indeed, the Ancient Egyptian civilization was one of the longest in the west, beginning in approximately 3000 B.C., and lasting until nearly 300 B.C.

Pharaoh's authority in the Ancient Egypt was great. The cult of the died pharaoh gained a huge importance in the Egyptian religion. The gigantic pyramids are constructed for preservation of the pharaoh body and his spirit and for extolling his authority. And not without reason these works of human hands fall into one of seven miracles of the World.According to many descriptions, these gigantic monoliths had earlier other view . They shined on the Sun by a white glaze of the polished calcareous tables on the background of many-pillar adjacent temples. Near to pharaoh's pyramids there were the pyramids of the wives and members of pharaoh's family.

It is clear, that the pyramids had steep "scientific contents " embodied in their forms, sizes and orientation on terrain. Each part of a pyramid, each element of the form was selected carefully and should demonstrate a high level of knowledge of the creators of pyramids. They were constructed on millennia, "for all time".

In the beginning of the 20th century in Saqqara (Egypt) archeologists had opened the crypt, in which the remnants of the Egyptian architect by name of Khesi-Ra were buried. The ancient texts informed us that Khesi-Ra was "a Chief of Destius and a Chief of Boot, a Chief of doctors, a writer of the pharaoh, a priest of Gor, a main architect of the pharaoh, a Supreme Chief of South Tens, and a carver". It is supposed that Khesi-Ra was the contemporary of Imhotep who lived in the period of the pharaoh Zoser (27th century BC) because in the crypt the printings of this pharaoh are found. There were 11 boards in the crypt.

A long time assigning of panels from Khesi-Ra crypt was vague. At first the Egyptologists accepted these panels for false doors. In the beginning of the 60`s it is noticed that there is the proportion on the panel.

Architect Khesi-Ra surrounded with different figures having the symbolical significance on all preserved panels is showed.

After the comprehensive and argued analysis by the method of proportions the Egyptologists get good causes to assert that Khesi-Ra's panels are the harmony rules encoded by geometry language:

So, in our hands we have the concrete material evidence, which shows us by "plain text" the highest level of abstract thought of the Ancient Egypt intellectuals. The artist cutting the panels with amazing accuracy, jeweler refinement and masterly ingenuity demonstrated the rule of the "Golden Section" in its broadest range of variations. As an outcome the "GOLDEN SYMPHONY", presented by the ensemble of the highly artistic works was born, which testifies not only ingenious talents of their creator, but also convincingly verifies that the author was familiar with the the secret of harmony. This genius was of the "Golden Business Craftsman" by the name of Khesi-Ra".

The orientation on the harmonic principle opened the path to a unprecedented flowering of culture for the Ancient Egypt civilization. This flowering falls to period of Zoser-pharaoh when the system of written signs was completely added up. Therefore it is possible, that the Zoser-pyramid became the first experimental pyramid designed under Khesi-Ra supervision.

The Great Pyramid of Giza is one of the oldest structures on the face of the Earth. The monument was supposedly built by the Egyptian Pharaoh Khufu of the Fourth Dynasty around the year BC 2560 to serve as a tomb when he died. It took 100,000 people working over a twenty year period to construct. The exact number of stones was orginally estimated at 2,300,000 stone blocks weighing from 2-30 tons each, with some weighing as much as 70 tons.

If we compare the pyramid cross-section in the next Diagram 1 to the construction in Diagram 2, we can see that side BC corresponds to 0.618034 of the radius, side AB corresponds to 0.78615, and side AC corresponds to 1. (As nearly as can now be determined, in actual Great Pyramid lengths, AB was equal to 481 feet, BC to 377.9 feet, and AC to 611.5 feet).

diagram 1
diagram 2

From here things begin to get really interesting . As can be seen, BC above is equal to one half the length of the pyramid's side. Therefore, the perimeter of the base equals BC x 8, and in relative terms this equals 0.618034 x 8 = 4.9443. The relative height of the pyramid is 0.78615, and, if one uses this length as the radius of a circle, then the circumference (perimeter) of that circle will also be 4.9443. Also, perhaps more important factor, is that the length of side OD (0.78615), when multiplied by 4 yields an amount (3.1446) that is almost exactly equal to Pi (3.1416). This finding means that the 38010' right triangle offers a unique and most interesting point of intersection between the Pi ratio and the golden ratio phenomenon. How this unexpected agreement comes to be is that :
As we saw in the 38010' right triangle, 0.618034 0.78615 = 0.78615. This means, that 0.618034 = 0.78615 x 0.78615. Therefore, 8 x 0.618034 is the same as 8 x 0.78615 x 0.78615;
As we also saw, 4 x 0.78615 is a very close approximation for Pi . Therefore,2*Pi can be said to equal 8 x .78615. For the circumference of the circle using 0.78615 as its radius, we then have C =2*Pi*R = (8 x 0.78615) x 0.78615 .
As a result, the Great Pyramid turns out to have the same perimeter length when measured in a horizontal plane, as a square, and in a vertical plane, as a circle.

        

        

        

        

        

  2001-2003 Radoslav Jovanovic              translated: D.Filipovic   created:  January 2003.