Editing Great Pyramid of Giza (section)

==Construction==

=== Preparation of the site ===
A hillock forms the base on which the pyramid stands. It was cut back into steps and only a strip around the perimeter was leveled,{{sfn|Lehner|Hawass|2017|p=214}} which has been measured to be horizontal and flat to within {{convert|21|mm|1|abbr=}}.{{sfn|Lehner|1997|p=109}} The bedrock reaches a height of almost {{Convert|6|m|ft}} above the pyramid base at the location of the Grotto.{{sfn|Maragioglio|Rinaldi|1965b}}

Along the sides of the base platform a series of holes are cut in the bedrock. Lehner hypothesizes that they held wooden posts used for alignment.<ref>{{Cite journal|last=Lehner|first=Mark|date=2016|title=In Search of the Human Hand that Built the Great Pyramid|url=http://www.aeraweb.org/wp-content/uploads/2018/01/AG17_1-2.pdf |archive-url=https://web.archive.org/web/20190801133158/http://www.aeraweb.org/wp-content/uploads/2018/01/AG17_1-2.pdf |archive-date=2019-08-01 |url-status=live|journal=Aeragram|volume=17|pages=20–23}}</ref> Edwards, among others, suggested the use of water for evening the base, although it is unclear how practical and workable such a system would be.{{sfn|Lehner|Hawass|2017|p=214}}

=== Materials ===
{{Location map+ | Egypt
| relief = 1
| width = 300
| caption = Origins of the materials used for Khufu's pyramid complex
| places =
  {{Location map~ | Egypt
      | label = [[Wadi Maghareh]]<br />(copper)
      | position = right
      | background = white 
      | label_width = 150
      | lat_deg = 28.8973
      | lon_deg = 33.3726
      | marksize = 13
  }}
  {{Location map~ | Egypt
      | label = [[Aswan]] (granite)
      | position = right
      | background = white 
      | label_width = 150
      | lat_deg = 24.077
      | lon_deg = 32.895
      | marksize = 13
  }}
  {{Location map~ | Egypt
      | label = Lebanon (timber)
      | position = bottom
      | background = white 
      | label_width = 150
      | lat_deg = 32
      | lon_deg = 35
      | marksize = 13
  }}
  {{Location map~ | Egypt
      | label = [[Giza]] (limestone)
      | position = top
      | background = white 
      | label_width = 150
      | lat_deg = 29.974
      | lon_deg = 31.135
      | marksize = 13
  }}
  {{Location map~ | Egypt
      | label = [[Tura, Egypt|Tura]] (white limestone)
      | position = right
      | background = white 
      | label_width = 150
      | lat_deg = 29.8528
      | lon_deg = 31.3458
      | marksize = 13
  }}
  {{Location map~ | Egypt
      | label = Widan el-Faras (basalt)
      | position = left
      | background = white 
      | label_width = 150
      | lat_deg = 29.657250
      | lon_deg = 30.625710
      | marksize = 13
  }}
}}
The Great Pyramid consists of an estimated 2.3&nbsp;million blocks. Approximately 5.5&nbsp;million tonnes of [[limestone]], 8,000&nbsp;tonnes of [[granite]], and 500,000&nbsp;tonnes of mortar were used in the construction.{{sfn|Romer|2007|p=157}}

Most of the blocks were [[Quarry|quarried]] at Giza just south of the pyramid, an area now known as the [[Central Field, Giza|Central Field]].<ref>{{Cite web|title=The Great Pyramid Quarry « Ancient Egypt Research Associates|date=14 October 2009|url=http://www.aeraweb.org/gpmp-project/great-pyramid-quarry/|access-date=2021-03-21|language=en-US}}</ref> They are a particular type of [[Nummulite|nummulitic limestone]] formed of the fossils of prehistoric shell creatures, whose small disc form can still be seen in some of the pyramid's blocks upon close inspection.<ref>Kaplan, Sarah, ''[https://s2.washingtonpost.com/camp-rw/?e=d3AucmVhZGVya0BnbWFpbC5jb20%3D&s=5aa036bcfe1ff62bafa91c52 Brilliance without a brain] {{Webarchive|url=https://web.archive.org/web/20180308103700/https://s2.washingtonpost.com/camp-rw/?e=d3AucmVhZGVya0BnbWFpbC5jb20%3D&s=5aa036bcfe1ff62bafa91c52|date=2018-03-08}}'', Speaking of Science, The Washington Post, March 7, 2018</ref> Other fossils have been found in the blocks and other structures on the site, including fossilized shark teeth.<ref>{{Cite web |title=Digital Giza {{!}} Fossilized shark's tooth |url=http://giza.fas.harvard.edu/objects/15290/full/ |access-date=2023-01-23 |website=giza.fas.harvard.edu}}</ref><ref>{{Cite web |title=Digital Giza {{!}} Western Cemetery: Site: Giza; View: G 2100-I |url=http://giza.fas.harvard.edu/photos/50574/full/ |access-date=2023-01-23 |website=giza.fas.harvard.edu}}</ref> The white limestone used for the casing was transported by boat across the Nile from the [[Tura, Egypt|Tura]] quarries of the [[Eastern Desert]] plateau, about {{Convert|10|km|abbr=on}} south-east of the Giza plateau. In 2013, rolls of papyrus called the [[Diary of Merer]] were discovered, written by a supervisor of the deliveries of limestone from Tura to Giza in the 27th year of Khufu's reign.<ref>{{Cite web|last=Stille|first=Alexander|title=The World's Oldest Papyrus and What It Can Tell Us About the Great Pyramids|url=http://www.smithsonianmag.com/history/ancient-egypt-shipping-mining-farming-economy-pyramids-180956619|url-status=live|archive-url=https://web.archive.org/web/20150928173821/http://www.smithsonianmag.com/history/ancient-egypt-shipping-mining-farming-economy-pyramids-180956619/|archive-date=28 September 2015|access-date=27 September 2015}}</ref>

The granite stones in the pyramid were transported from [[Aswan]], more than {{convert|900|km|mi|abbr=on}} south.{{sfn|Lehner|1997|p=207}} The largest, weighing 25 to 80 tonnes, form the ceilings of the "King's chamber" and the "relieving chambers" above it. Ancient Egyptians cut stone into rough blocks by hammering grooves into natural stone faces, inserting wooden wedges, then soaking these with water. As the water was absorbed, the wedges expanded, breaking off workable chunks. Once the blocks were cut, they were carried by boat on the [[Nile]] to the pyramid and used a now dry offshoot of the river to transport blocks closer to the site.{{sfn|Lehner|1997|p=202}}<ref>{{cite web | url=https://edition.cnn.com/2022/09/02/world/nile-river-egypt-pyramid-scn-trnd/index.html#:~:text=This%20explanation%2C%20known%20as%20the,down%20to%20the%20river%27s%20bottom. | title=A now-dry branch of the Nile helped build Egypt's pyramids, study says | date=2 September 2022 }}</ref>

=== Workforce ===
The [[Ancient Greece|ancient Greeks]] believed that [[Slavery in ancient Egypt|slave labour]] was used, but modern discoveries made at nearby workers' camps associated with construction at Giza suggest that it was built by thousands of [[Civil conscription|conscript labourers]].{{sfn|Lehner|1997|pp=39, 224}}

Worker graffiti found at Giza suggest haulers were divided into ''zau'' (singular ''za''), groups of 40 men, consisting of four sub-units that each had an "Overseer of Ten".<ref>{{Cite journal|last=Lehner|first=Mark|date=2004|title=Of Gangs and Graffiti: How Ancient Egyptians Organized their Labor Force|url=http://www.aeraweb.org/wp-content/uploads/2015/01/aeragram7_1.pdf|journal=Aeragram|volume=7-1|pages=11–13|access-date=27 March 2021|archive-date=22 April 2021|archive-url=https://web.archive.org/web/20210422084726/http://www.aeraweb.org/wp-content/uploads/2015/01/aeragram7_1.pdf|url-status=dead}}</ref>{{sfn|Tallet|2017}}

As to the question of how over two million blocks could have been cut within Khufu's lifetime, stonemason Franck Burgos conducted an [[Experimental archaeology|archaeological experiment]] based on an abandoned quarry of Khufu discovered in 2017. Within it, an almost completed block and the tools used for cutting it had been uncovered: hardened [[Arsenical bronze|arsenic copper]] chisels, wooden mallets, ropes and stone tools. In the experiment replicas of these were used to cut a block weighing about 2.5 tonnes (the average block size used for the Great Pyramid). It took four workers 4 days (with each working 6 hours a day) to excavate it. The initially slow progress speeded up six times when the stone was wetted with water. Based on the data, Burgos extrapolates that about 3,500 quarry-men could have produced the 250 blocks/day needed to complete the Great Pyramid in 27 years.<ref>{{Cite journal|last1=Burgos|first1=Franck|last2=Laroze|first2=Emmanuel|date=2020|title=L'extraction des blocs en calcaire à l'Ancien Empire. Une expérimentation au ouadi el-Jarf|url=http://www.egyptian-architecture.com/JAEA4/article27/JAEA4_Burgos_Laroze.pdf |archive-url=https://web.archive.org/web/20210627235809/http://www.egyptian-architecture.com/JAEA4/article27/JAEA4_Burgos_Laroze.pdf |archive-date=2021-06-27 |url-status=live|journal=Ancient Egyptian Architecture|volume=4|pages=73–95}}</ref>

A construction management study conducted in 1999, in association with [[Mark Lehner]] and other Egyptologists, had estimated that the total project required an average workforce of about 13,200 people and a peak workforce of roughly 40,000.<ref name="civilengineer2">{{cite magazine|last=Smith|first=Craig B.|date=June 1999|title=Project Management B.C.|url=http://www.pubs.asce.org/ceonline/0699feat.html|url-status=dead|magazine=Civil Engineering Magazine|volume=69|issue=6|archive-url=https://web.archive.org/web/20070608101037/http://www.pubs.asce.org/ceonline/0699feat.html|archive-date=8 June 2007}}</ref>

=== Surveys and design ===
{{Comparison of pyramids.svg|ku|upright=1.4}}
The first precise measurements of the pyramid were made by Egyptologist [[Flinders Petrie]] in 1880–1882, published as ''The Pyramids and Temples of Gizeh''.{{sfn|Petrie|1883}} Many of the casing-stones and inner chamber blocks of the Great Pyramid fit together with high precision, with joints, on average, only {{convert|0.5|mm|inch}} wide.<ref>{{cite book|author=I.E.S. Edwards|title=The Pyramids of Egypt|year=1986|page=285|author-link=I.E.S. Edwards|orig-year=1947}}</ref> In contrast, core blocks were only roughly shaped, with rubble inserted between larger gaps. Mortar was used to bind the outer layers together and fill gaps and joints.<ref name="Fabric" />

The block height and weight tends to get progressively smaller towards the top. Petrie measured the lowest layer to be {{Convert|148|cm|ft}} high, whereas the layers towards the summit barely exceed {{Convert|50|cm|ft}}.{{sfn|Petrie|1883}}

The accuracy of the pyramid's perimeter is such that the four sides of the base have an average error of only {{convert|58|mm|in|abbr=off}} in length{{efn|1=Based on side lengths 230.252&nbsp;m, 230.454&nbsp;m, 230.391&nbsp;m, 230.357&nbsp;m.{{sfnp|Cole|1925}}}} and the finished base was squared to a mean corner error of only 12&nbsp;[[Minute and second of arc|seconds of arc]].{{sfn|Petrie|1883|p=38}}

The completed design dimensions are measured to have originally been {{convert|280|royal cubit|m+ft|1|lk=in}} high by {{convert|440|royal cubit|m+ft|1|bits (|)|abbr=on|disp=x}} long at each of the four sides of its base. Ancient Egyptians used [[seked]] – how much run for one cubit of rise – to describe slopes. For the Great Pyramid a seked of {{sfrac|5|1|2}} palms was chosen, a ratio of 14&nbsp;up to 11&nbsp;in.{{sfn|Lehner|1997|p=218}}

Some Egyptologists suggest this slope was chosen because the ratio of perimeter to height (1760/280 cubits) equals 2[[pi|π]] to an accuracy of better than 0.05&nbsp;percent (corresponding to the well-known approximation of π as 22/7). Verner wrote, "We can conclude that although the ancient Egyptians could not precisely define the value of π, in practice they used it".{{sfn|Verner|2003|p=70}} Petrie concluded: "but these relations of areas and of circular ratio are so systematic that we should grant that they were in the builder's design".{{sfnp|Petrie |1940|p=30}} Others have argued that the ancient Egyptians had no concept of pi and would not have thought to encode it in their monuments and that the observed pyramid slope may be based on the [[seked]] choice alone.{{sfnp|Rossi|2007|p={{page needed|date=August 2020}}}}

==== Alignment to the cardinal directions ====
The sides of the Great Pyramid's base are closely aligned to the four geographic (not magnetic) cardinal directions, deviating on average [[Minute and second of arc|3 minutes and 38 seconds of arc]], or about a tenth of a [[Degree (angle)|degree]].<ref>{{Cite journal|last=Dash|first=Glen|date=2012|title=New Angles on the Great Pyramid|url=http://www.aeraweb.org/wp-content/uploads/2015/01/aeragram13_2.pdf |archive-url=https://web.archive.org/web/20160402181457/http://www.aeraweb.org/wp-content/uploads/2015/01/aeragram13_2.pdf |archive-date=2016-04-02 |url-status=live|journal=Aeragram|volume=13-2|pages=10–19}}</ref> Several methods have been proposed for how the ancient Egyptians achieved this level of accuracy:

* The solar [[gnomon]] method: The shadow of a vertical rod is tracked throughout a day. The shadow line is intersected by a circle drawn around the base of the rod. Connecting the intersecting points produces an east–west line. An experiment using this method resulted in lines being, on average, 2&nbsp;minutes, 9&nbsp;seconds off due east–west. Employing a pinhole produced much more accurate results (19&nbsp;arc seconds off), whereas using an angled block as a shadow definer was less accurate (3′&nbsp;47″ off).<ref>{{Cite journal|last=Dash|first=Glen|date=2014|title=Did Egyptians Use the Sun to Align the Pyramids?|url=http://www.aeraweb.org/wp-content/uploads/2015/09/AG15_1_2.pdf |archive-url=https://web.archive.org/web/20160402200158/http://www.aeraweb.org/wp-content/uploads/2015/09/AG15_1_2.pdf |archive-date=2016-04-02 |url-status=live|journal=Aeragram|volume=15|pages=24–28}}</ref>
* The [[pole star]] method: The polar star is tracked using a movable sight and fixed plumb line. Halfway between the maximum eastern and western elongations is true north. [[Thuban]], the polar star during the Old Kingdom, was about two degrees removed from the celestial pole at the time.<ref>{{Cite web|title=How the Pyramid Builders May Have Found Their True North Part II: Extending the Line|url=http://glendash.com/blog/2014/06/20/how-the-pyramid-builders-may-have-found-their-true-north-part-ii-extending-the-line-2/|access-date=8 April 2021|archive-date=8 December 2021|archive-url=https://web.archive.org/web/20211208024645/http://glendash.com/blog/2014/06/20/how-the-pyramid-builders-may-have-found-their-true-north-part-ii-extending-the-line-2/|url-status=dead}}</ref>
* The simultaneous transit method: The stars [[Mizar]] and [[Kochab]] appear on a vertical line on the horizon, close to true north around 2500&nbsp;BC. They slowly and simultaneously shift east over time, which is used to explain the relative misalignment of the pyramids.<ref name="Spence2000"/><ref>{{Cite journal|last=Dash|first=Glen|date=2015|title=Simultaneous Transit and Pyramid Alignments: Were the Egyptians' Errors in Their Stars or in Themselves?|url=http://dashfoundation.com/downloads/archaeology/working-papers/Simultaneous_Transit.pdf|journal=Glen Dash Foundation for Archaeological Research|archive-url=https://web.archive.org/web/20200327154119/http://glendash.com/downloads/archaeology/working-papers/Simultaneous_Transit.pdf|archive-date=27 March 2020}}</ref>

===Construction theories===
{{Main|Egyptian pyramid construction techniques}}
Many alternative, often contradictory, theories have been proposed regarding the pyramid's construction techniques.<ref>{{cite web|date=3 February 2006|title=Building the Great Pyramid|url=https://www.bbc.co.uk/history/ancient/egyptians/great_pyramid_01.shtml|url-status=live|archive-url=https://web.archive.org/web/20090205042037/http://www.bbc.co.uk/history/ancient/egyptians/great_pyramid_01.shtml|archive-date=5 February 2009|access-date=5 April 2009|publisher=BBC}}</ref> One mystery of the pyramid's construction is its planning. [[John Romer (Egyptologist)|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 precision unmatched by any other means".{{sfn|Romer|2007|pp=327, 329–337}}

The basalt blocks of the pyramid temple show "clear evidence" of having been cut with some kind of saw with an estimated cutting blade of {{convert|15|ft|m}} in length. Romer suggests that this "super saw" may have had copper teeth and weighed up to {{convert|140|kg|lb}}. He theorizes that such a saw could have been attached to a wooden [[trestle support]] and possibly used in conjunction with vegetable oil, cutting sand, [[Emery (rock)|emery]] or pounded quartz to cut the blocks, which would have required the labour of at least a dozen men to operate it.{{sfn|Romer|2007|pp=164, 165}}