Building the pyramid
It is believed 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 originally 280 Egyptian 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 in length, (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. 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. 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 0.5 millimeters wide (1/50th of an inch).
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 mean error of only 58 millimeter in length  The base is horizontal and flat to within 15 mm. The sides of the square base are closely aligned to the four cardinal compass points (within 4 minutes of arc) based on true north, not magnetic north, and the finished base was squared to a mean corner error of only 12 seconds of arc. 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 π/2 to an accuracy of better than 0.05% (corresponding to the approximation of π as 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 π, 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 approximately 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 .
- See also: Calculating the weight of megaliths
The Great Pyramid consists of more than 2.3 million limestone blocks. The Egyptians obtained the majority of the limestone blocks from a nearby quarry. The Tufa limestone used for the casing was quarried across the river. The largest granite stones in the pyramid, found in the "King's" chamber, weigh 25 to 80 tonnes and were transported more than 500 miles away from Aswan. Traditionally, ancient Egyptians cut stone blocks by hammering wedges into the stone which were then 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. 
At completion, the Great Pyramid was surfaced by white 'casing stones' – slant-faced, but flat-topped, blocks of highly polished white limestone. These were carefully cut to what is approximately 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. Petrie related the precision of the casing stones as to being "equal to opticians' work of the present day, but on a scale of acres." and "to place such stones in exact contact would be careful work; but to do so with cement in the joints seems almost impossible."
Many alternative, often contradictory, theories have been proposed regarding the Pyramid's construction techniques. Not all even agree that the blocks were quarried, they might conceivably have been cast. However, most accept it was built by moving huge stones from a quarry, being only unable to agree whether they were dragged, lifted or even rolled into place. The Greeks believed that slave labour was used but modern Egyptologists accept that it was built by many tens of thousands of skilled workers. They camped near the pyramids and worked for a salary or as a form of paying taxes until the construction was completed. Their cemeteries were discovered in 1990 by archaeologists Zahi Hawass and Mark Lehner. Verner posited that the labor was organized into a hierarchy, consisting of two gangs of 100,000 men, divided into five zaa or phyle of 20,000 men each, which may have been further divided according to the skills of the workers.
One of the mysteries of the pyramid's construction is how they planned its construction. John Romer suggests that they used the same method that had been used for earlier and later constructions, laying out parts of the plan on the ground at a 1 to 1 scale. He writes that "such a working diagram would also serve to generate the architecture of the pyramid with a precision unmatched by any other means." He devotes a chapter of his book to the physical evidence that there was such a plan.
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.
Today, tourists enter the Great Pyramid via a forced tunnel dug by the Caliph Al-Ma'mum and his men around 820 AD. The tunnel continues for approximately 30 meters and eventually meets up with the Descending Passage which at the time was found to have been blocked by a series of massive granite plugs. Unable to remove the blocks, the workmen tunneled around the plugs discovering the Ascending Passage which leads to the Grand Gallery and interior chambers only to find them empty. The original entrance, which was apparently unknown at the time, can be seen today several meters directly above the forced entry and would have also been blocked by the granite plugs.
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 granite room was originally 10 × 20 × 11.4 cubits, or about 5.235 m × 10.47 m × 5.974 m, comprising a double 10 × 10 cubit square floor, and a height equal to half the double square's diagonal. Some believed that the height was consistent with the geometric methods for determining the Golden Ratio φ (phi) as the height is approximately phi times the width minus ½, while phi can be derived from other dimensions of the pyramid, but evidence from Petrie’s surveys and later conclusions drawn by others shows that it was in fact the circular proportions that were deliberately incorporated into the internal and external designs of the Great Pyramid by its architects and builders, for symbolic reasons. The so called golden ratio phi simply exists in the proportions of the architecture as an inadvertent by-product of the inclusion of the circular proportions. The reason for the inadvertent inclusion is that phi, the golden ratio, has a naturally occurring mathematical relation to the circular ratio pi that is unrelated to the architecture or geometry, and which was unknown to the pyramids builders. Petrie confirmed that the King’s Chamber was a triumph of Egyptian geometry, the ratio of its length to the circuit of the side wall being the same as the ratio of 1 to pi, and that the exterior of the pyramid had been built to the same proportions
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. Despite being originally discovered closed off at both ends, these shafts were once thought by Egyptologists to have been used as "ventilation shafts", but this idea was eventually abandoned, leaving them 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 of 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.
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.
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.
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. One of the small pyramids contains the tomb of queen Hetepheres (discovered in 1925), sister and wife of Sneferu and the mother of Khufu. There was a town for the workers of Giza, which included a cemetery, bakeries, a beer factory and a copper smelting complex. A few hundred meters south-west of the Great Pyramid lies the slightly smaller Pyramid of Khafre, one of Khufu's successors who is also commonly considered the builder of the Great Sphinx, and a few hundred meters further south-west is the Pyramid of Menkaure, Khafre's successor, which is about half as tall. In May 1954, 41 blocking stones were uncovered close to the south side of the Great Pyramid. They covered a 30.8 meter long rock-cut pit that contained the remains of a 43 meter long ship of cedar wood. In antiquity, it had been dismantled into 650 parts comprising 1224 pieces. This funeral boat of Khufu has been reconstructed and is now housed in a museum on the site of its discovery. A second boat pit was later discovered nearby.