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The Great Pyramid of Giza


The Great Pyramid of Giza, in 2005. Believed to be built c. 2560 BCE., it is the oldest and largest of the three 
pyramids in the Giza Necropolis.

The Great Pyramid of Giza (also called the Khufu's Pyramid, Pyramid of Khufu, and Pyramid of Cheops, its Greek name) is the oldest and largest of the three pyramids in the Giza Necropolis bordering what is now Cairo, Egypt, and is the only one of the Seven Wonders of the Ancient World that survives substantially intact. It is believed by some that the pyramid was built as a tomb for Fourth dynasty Egyptian King Khufu (Cheops in Greek) and constructed over a 20 year period concluding around 2560 BC. The Great Pyramid was the tallest man-made structure in the world for over 3,800 years. Originally the Great Pyramid was covered by casing stones that formed a smooth outer surface, and what is seen today is the underlying core structure. Some of the casing stones that once covered the structure can still be seen around the base. There have been varying scientific and alternative theories regarding the Great Pyramid's construction techniques. Most accepted construction theories are based on the idea that it was built by moving huge stones from a quarry and dragging and lifting them into place.

There are three known chambers inside the Great Pyramid. The lowest chamber is cut into the bedrock upon which the pyramid was built and was unfinished. The so-called Queen's Chamber and King's Chamber are higher up within the pyramid structure. The Great Pyramid of Giza is the main part of a complex setting of buildings that included two mortuary temples in honor of Khufu (one close to the pyramid and one near the Nile), three smaller pyramids for Khufu's wives, an even smaller "satellite" pyramid, a raised causeway connecting the two temples, and small mastaba tombs surrounding the pyramid for nobles.

Building the Pyramid

This magnificent remnant of ancient wisdom is constructed of about 2.3 million stone blocks of mostly limestone from quarries across the Nile weighing on the average about 2 1/2 tons each (2200 kilograms), placed in 203 courses on exactly 13 acres (5.3 hectare) of perfectly square land, that still today is only off absolute perfect center by a 1/4 inch. Granite blocks of 70 tons each (64,000 kilograms) were brought 500 miles (800 kilometers) down the Nile from Aswan for the King's chamber. Fine white limestone casing stones 5 feet (1 1/2 meter) high, 12 feet (3 1/3 meters) long and 8 feet (2.4 meters) wide, some weighing 15 tons (13,000 kilograms), were fitted to enclose the entire structure, a surface area of aprox. 22 acres (8.9 hectare). The sides of the casing stones are filled with mortar, the composition of which is still uncertain. These sides are so straight and square that the gap between them is 1/50 of an inch (.01 cm). The mean variation of the surface of the casing stones from perfectly straight is 1/100 inch over 75 inches (.004 cm over almost 2 meters) as determined by W.F. Petrie from the few examples found at its' base. It is unknown but probable that this precision was continued through-out the 22 acres of Pyramid surface. Sir William Flinders Petrie is considered the founder of modern scientific archeology. Mainstream archeology has a high regard for his results.

The Great Pyramid's foundation of fine limestone blocks is within 7/8 inch (2 cm) of true level, and even that small inaccuracy could be the result of subsidence of a portion of the plateau due to the weight of the Pyramid or earthquakes. There is a slight hollowing of all four sides of the Great Pyramid, which escaped notice until Petrie found it in his survey of 1881. The indentation is at its greatest on the northern side where the center of the face is set back 37 inches (94 cm). This perhaps was to make the monument stronger, to improve its' appearance, or perhaps some more esoteric reason. One certainty - if the hollowing was carried to the casing stones the difficulty of maintaining the extreme precision with which they were faced increases still further. The first 150 feet (46 meters) of the descending passage, where it goes through the masonry of the Pyramid, is within 1/50 of an inch (.01 cm) of perfectly straight and the remaining 200 feet (60 meters), which is cut into natural rock, deviates only 1/4 inch (.4 cm). (Petrie) Petrie determined that stone was cut by saws with blades about 9 feet (2.7 meters) long, with hard jewels such as diamond or corundum on the cutting tips. To drill out the interior of the sarcophagus (which is a single piece of very hard granite) a drill was used with a pressure of two tons, an extraordinary amount of pressure.

The Mathematics of the Great Pyramid

Many relationships between the Great Pyramid and various factors have been theorized. Some may be intentional, others may be coincidence. Even pared down to the few correlations specified by ancient authors and verified by modern measurement, it is clear that the Pyramid represents a unique geometric figure attainable only by a highly evolved mathematics. The height to perimeter ratio is pi ( "p" ) (Smyth: 3.14159+) (Petrie: 3.1428+). This relationship is basic to this particular Pyramid form and no other. It establishes a direct relationship between the Pyramid and a half sphere - and thus with the Northern Hemisphere of our planet. Agatharchides of Cnidus was a guardian and philosopher in the court of the king of Egypt at the end of the second century BCE. From sources available to him he reported that the base of the Great Pyramid was 1/8 minute of latitude. This has been proven correct by modern measurement to within a tenth of a percent. The Faces of all Pyramids are aligned to North, East, South and West. The alignment of the Great Pyramid deviates from true on two corners by three minutes, on one by thirty seconds and the fourth by only two seconds. While there are theories that account for the variance as intentional, as it stands the Great Pyramid is extraordinarily precise in its alignment.

Precession of the Equinoxes

The tilt of the earth is not fixed but rotates relative to the stars at the very slow pace of about one turn every 26,000 years. This creates the great ages of Astrology, each constellation in turn taking its place on the horizon at dawn. Currently we are entering the Age of Aquarius (there is no agreement of the exact date of change, indeed it is a gradual transition). We are leaving the age of Pisces. The cult of the bull (Apis) was prominent in early Egyptian history, to be largely replaced by that of the ram (Amun) as the constellation Aries moved to the equinoctial position on the horizon following Taurus. One degree of movement in the precession takes about 72 years. Knowledge of such a slow movement of the heavens shows a highly developed mathematical astronomy at the earliest stages of known Egyptian history.

More Sacred Geometry

for the mathematics minded
The triangle formed by the Great Pyramid's height, apothem (linear height of one face) and half the width of the base - in other words a cross section of half the Pyramid - shows that the Egyptians incorporated Phi ("f" - the golden section - considered the most harmonious relationship in art and of great mystical significance) into the design. If the half base is considered to have the length of one unit then the apothem has a length of f and the height is the square root of f. This modern measurement, correct to at least 4 digits, proves the information given to Herodotus who was told by Egyptian priests that the area of each face was equal to the square of the Pyramid's height. (Height: square root of f squared = f X 1/2 base [defined as 1] = f) The Great Pyramid does not stand in historical isolation. While the Great Pyramid is the largest, and by most accounts the most accurate, there has been little study of the geometry and accuracy of the other fourth dynasty Pyramids. It is likely that the other Pyramids of this era also contain mathematical principles and intentional relationships, perhaps including some important ideas that modern science is currently unaware of. Egyptian temples were reflections of the gods that they served, using sacred geometry to evoke specific energies. Perhaps eventual research will find very specific explanations for the positions, size and angles of the other major Pyramids.

It is believed by some that the pyramid was built as a tomb for Fourth dynasty Egyptian pharaoh Khufu and constructed over a 14 to 20 year period concluding around 2560 BC. Khufu's vizier, Hemon, or Hemiunu, is believed by some to be the architect of the Great Pyramid. It is thought that, at construction, the Great Pyramid was 280 Egyptian royal cubits tall, 146.6 meters, (480.97 feet, or about 40 stories) but with erosion and the loss of its pyramidion, its current height is 138.8 m (455 feet). Each base side was 440 royal cubits, 230.5 meters, (756.2 feet). A royal cubit measures 0.524 meters. The total mass of the pyramid is estimated at 5.9 million tonnes. The volume, including an internal hillock, is believed to be roughly 2,500,000 cubic meters. Based on these estimates building this in 20 years would involve installing approximately 800 tonnes of stone every day. Manetho gives Khufu a reign of 65 years on his kings list, this would enable him to build the pyramid by moving only 250 tonnes of stone per day. The first precision measurements of the pyramid were done by Egyptologist Sir Flinders Petrie in 1880–82 and published as The Pyramids and Temples of Gizeh. Almost all reports are based on his measurements. Petrie found the pyramid is oriented 4' west of North and the second pyramid is similarly oriented. Many of the casing stones and interior chamber blocks of the great pyramid were fit together with extremely high precision. Based on measurements taken on the north eastern casing stones, the mean opening of the joints are only 1/50th of an inch wide.


Great Pyramid of Giza from a 19th century. The pyramid remained the tallest man-made structure in the world for over 3,800 years, unsurpassed until the 160 meter tall spire of Lincoln Cathedral was completed c. 1300. The accuracy of the pyramid's workmanship is such that the four sides of the base have a been said to have a mean error of only 58 millimeter in length, and 1 minute in angle from a perfect square. The base is horizontal and flat to within 15 mm. The sides of the square are closely aligned to the four cardinal compass points (within 3 minutes of arc based on true north not magnetic north). The completed design dimensions, as suggested by Petrie's survey and later studies, are estimated to have originally been 280 cubits in height by 440 cubits in length at each of the four sides of its base. These proportions equate to p/2 to an accuracy of better than 0.05% (corresponding to the approximation of p as roughly 22/7). Some Egyptologists consider this to have been the result of deliberate design proportion. Verner wrote, "We can conclude that although the ancient Egyptians could not precisely define the value of p, in practise they used it". Petrie, author of ‘The Pyramids and Temples of Gizeh', who was the first accurate surveyor of Giza and the excavator and surveyor of the Pyramid of Meidum, concluded: "but these relations of areas and of circular ratio are so systematic that we should grant that they were in the builders design". Earlier in the chapter he wrote more specifically, that: “We conclude therefore that the approximation of 7 to 22 as the ratio of diameter to circumference was recognised”. These proportions equated to the four outer faces sloping by precisely 51.842º or 51º 50' 35", which would have been understood and expressed by the Ancient Egyptians as a seked slope of 5 1/2 palms

Materials:

The Great Pyramid consists of more than 2.3 million limestone blocks. The Egyptians shipped the limestone blocks from quarries all along the Nile River. The stone was cut by hammering wedges into the stone. Then, the wedges were soaked with water. The wedges expanded, causing the rock to crack. Once they were cut, they were carried by boat either up or down the Nile River to the pyramid.


Khufu Pyramid casing stone

Casing stones:

casing stoneAt completion, the Great Pyramid was surfaced by white 'casing stones' – slant-faced, but flat-topped, blocks of highly polished white limestone. These were carefully and consistently cut with a face slope with a seked of 5 1/2 palms to give the required overall dimensions. Visibly all that remains is the underlying step-pyramid core structure seen today. In AD 1301, a massive earthquake loosened many of the outer casing stones, which were then carted away by Bahri Sultan An-Nasir Nasir-ad-Din al-Hasan in 1356 in order to build mosques and fortresses in nearby Cairo. The stones can still be seen as parts of these structures to this day. Later explorers reported massive piles of rubble at the base of the pyramids left over from the continuing collapse of the casing stones, which were subsequently cleared away during continuing excavations of the site. Nevertheless, many of the casing stones can be seen to this day in situ around the base of the Great Pyramid, and display the same workmanship and precision as has been reported for centuries. Petrie also found a different orientation in the core and in the casing measuring 193 centimeters ± 25 centimeters. He suggested a redetermination of north was made after the construction of the core, but a mistake was made, and the casing was built with a different orientation.

Interior:

The Great Pyramid is the only pyramid known to contain both ascending and descending passages. There are three known chambers inside the Great Pyramid. These are arranged centrally, on the vertical axis of the pyramid. From the entrance, an 18 meter corridor leads down and splits in two directions. One way leads to the lowest and unfinished chamber. This chamber is cut into the bedrock upon which the pyramid was built. It is the largest of the three, but totally unfinished, only rough-cut into the rock. The other passage leads to the Grand Gallery (49 m x 3 m x 11 m), where it splits again. One tunnel leads to the Queen's Chamber, a misnomer, while the other winds to intersect with the descending corridor. The Grand Gallery itself features a corbel haloed design and several cut "sockets" spaced at regular intervals along the length of each side of its raised base with a "trench" running along its center length at floor level. What purpose these sockets served is unknown. An antechamber leads from the Grand Gallery to the King's Chamber.

King's Chamber:

At the end of the lengthy series of entrance ways leading into the interior is the structure's main chamber, the King's Chamber. This chamber was originally 10 × 20 × 11.2 cubits, or about 5.25 m × 10.5 m × 6 m, comprising a double 10 × 10 cubit square, and a height equal to half the double square's diagonal. Some believe that this is consistent with the geometric methods for determining the Golden Ratio f (phi), which can be derived from other dimensions of the pyramid, such that if f had been the design objective, then p automatically follows to 'square the circle'.

The sarcophagus of the King's Chamber was hollowed out of a single piece of Red Aswan granite and has been found to be too large to fit through the passageway leading to the chamber. Whether the sarcophagus was ever intended to house a body is unknown. It is too short to accommodate a medium height individual without the bending of the knees, a technique not practiced in Egyptian burial, and no lid has ever been found. The King's Chamber contains two small shafts that ascend out of the pyramid. These shafts were once thought to have been used for ventilation, but this idea was eventually abandoned, which left Egyptologists to conclude they were instead used for ceremonial purposes. It is now thought that they were to allow the Pharaoh's spirit to rise up and out to heaven.

The King's Chamber is lined with red granite brought from Aswan 935 km (580 miles) to the south. There are 5 relieving chambers above the kings chamber. The first one is reached through a breach in the wall at the upper end of the Grand Gallery, this was named the Davidson chamber. Howard Vyse suspected there was another chamber above this when he found that he was able to thrust a long reed through a crack in the ceiling. He blasted through to find 4 more relieving chambers. These chambers were named the Wellington, Nelson, Lady Arbuthnot and Cambell's chambers. The kings chamber and the first 4 relieving chambers have roofs made out granite. Each roof includes 8 or 9 granite slabs weighing 25 to 80 tonnes each. Cambell's chamber has a pented roof made of large limestone slabs. Egyptologists believe they were transported on barges down the Nile river.

Queen's Chamber:

The Queen's Chamber is the middle and the smallest, measuring approximately 5.74 by 5.23 meters, and 4.57 meters in height. The chamber is lined with fine limestone blocks and the pented roof is made of large limestone slabs. Its eastern wall has a large angular doorway or niche. Egyptologist Mark Lehner believes that the Queen's chamber was intended as a serdab, a structure found in several other Egyptian pyramids, and that the niche would have contained a statue of the interred. The Ancient Egyptians believed that the statue would serve as a "back up" vessel for the Ka of the Pharaoh, should the original mummified body be destroyed. The true purpose of the chamber, however, remains uncertain. The Queens Chamber has a pair of shafts similar to those in the King's Chamber, which were explored using a robot, Upuaut 2, created by the German engineer Rudolf Gantenbrink. In 1992, Upuaut 2 discovered that these shafts were blocked by limestone "doors" with two eroded copper handles. The National Geographic Society filmed the drilling of a small hole in the southern door, only to find another larger door behind it. The northern passage, which was harder to navigate due to twists and turns, was also found to be blocked by a door.

Unfinished chamber:

The "unfinished chamber" lies 27.5 meters below ground level and is rough-hewn, lacking the precision of the other chambers. Egyptologists suggest the chamber was intended to be the original burial chamber, but that King Khufu later changed his mind and wanted it to be higher up in the pyramid. Egyptologist Bob Brier believes it was an insurance policy in case Khufu died early. When he was still alive and healthy after about 5 years of construction, the second (Queen's) chamber was begun. Sometime around the fifteenth year this chamber was also abandoned unfinished and the last or King's Chamber was built high up in the center of the pyramid.

References

  1. "Secrets of the Great Pyramid" by Peter Tompkins, appendix by Livio Catullo Stecchini.
  2. Bauval, Robert &, Hancock, Graham (1996). Keeper of Genesis. Mandarin books. ISBN 0-7493-2196-2.
  3. Brier, Bob &, Hobbs, A. Hoyt (1999). Daily Life of the Ancient Egyptians. Greenwood Press. ISBN 978-0313303135.
  4. Calter, Paul A. (2008). Squaring the Circle: Geometry in Art and Architecture. Key College Publishing. ISBN 1-930190-82-4.
  5. Clayton, Peter A. (1994). Chronicle of the Pharaohs. Thames & Hudson. ISBN 0-500-05074-0.
  6. Collins, Dana M. (2001). The Oxford Encyclopedia of Ancient Egypt. Oxford University Press. ISBN 9780195102345.
  7. Cremin, Aedeen (2007). Archaeologica. Frances Lincoln. ISBN 978-0711228221.
  8. Dilke, O.A.W. (1992). Mathematics and Measurement. University of California Press. ISBN 0520060725.
  9. Gahlin, Lucia (2003). Myths and Mythology of Ancient Egypt. Anness Publishing Ltd. ISBN 1-84215-831-7.
  10. Lehrner, Mark (1997). The Complete Pyramids. London: Thames and Hudson. ISBN 0-500-05084-8.
  11. Levy, Janey (2005). The Great Pyramid of Giza: Measuring Length, Area, Volume, and Angles. Rosen Publishing Group. ISBN 1404260595.
  12. Lepre, J.P. (1990). The Egyptian Pyramids: A Comprehensive, Illustrated Reference. McFarland & Company. ISBN 0899504612.
  13. Lightbody, David I (2008). Egyptian Tomb Architecture: The Archaeological Facts of Pharaonic Circular Symbolism. British Archaeological Reports International Series S1852. ISBN 978-1407303390.
  14. Oakes, Lorana; Lucia Gahlin (2002). Ancient Egypt. Hermes House. ISBN 1-84309-429-0.
  15. Petrie, Sir William Matthew Flinders (1883). The Pyramids and Temples of Gizeh. Field & Tuer. ISBN 0710307098.
  16. Romer, John (2007). The Great Pyramid: Ancient Egypt Revisited. Cambridge University Press, Cambridge. ISBN 978-0-521-87166-2.
  17. Scarre, Chris (1999). The Seventy Wonders of the Ancient World. Thames & Hudson, London. ISBN 978-0500050965.
  18. Seidelmann, P.Kenneth (1992). Explanatory Supplement to the Astronomical Almanac. University Science Books. ISBN 0-935702-68-7.
  19. Shaw, Ian (2003). The Oxford History of Ancient Egypt. Oxford University Press. ISBN 0198150342.
  20. Siliotti, Alberto (1997). Guide to the pyramids of Egypt; preface by Zahi Hawass.. Barnes & Noble Books. ISBN unknown.
  21. Smyth, Piazzi (1978). The Great Pyramid. Crown Publishers Inc.. ISBN 0-517-26403-X.
  22. Tyldesley, Joyce (2007). Egypt:How a lost civilization was rediscovered. BBC Books. ISBN 978-0563522577.
  23. Verner, Miroslav (2001). The Pyramids: The Mystery, Culture, and Science of Egypt's Great Monuments. Grove Press. ISBN 0-8021-1703-1.
  24. Verner, Miroslav (2003). The Pyramids: Their Archaeology and History. Atlantic Books. ISBN 1843541718.
  25. Wikipedia.org



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