Editing Great Pyramid of Giza (section)

=== 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>