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== Casing == [[File:Cheops pyramid 02.jpg|thumb|Remaining casing stones on the north side of the Great Pyramid]] [[File:KhufuPyramidCasingStone-BritishMuseum-August19-08.jpg|thumb|A casing stone in the [[British Museum]]<ref>{{cite web|title=British Museum β Limestone block from the pyramid of Khufu|url=https://www.britishmuseum.org/explore/highlights/highlight_objects/aes/l/limestone_block_from_the_pyram.aspx|url-status=live|archive-url=https://web.archive.org/web/20140727091314/https://www.britishmuseum.org/explore/highlights/highlight_objects/aes/l/limestone_block_from_the_pyram.aspx|archive-date=27 July 2014|access-date=30 June 2014|work=britishmuseum.org}}</ref>]]At completion, the Great Pyramid was cased entirely in white limestone. Precisely worked blocks were placed in horizontal layers and carefully fitted together with mortar, their outward faces cut at a slope and smoothed to a high degree. Together they created four uniform surfaces, angled at 51Β°50'40" (a [[seked]] of {{sfrac|5|1|2}} [[Palm (unit)#Ancient Egypt|palm]]s).<ref>The History of Mathematics: A Brief Course, by Roger L. Cooke; 2nd Edition; John Wiley & Sons, 2011; {{ISBN|9781118030240}}; pp. 235β236</ref><ref>The Pyramid Builder's Handbook; by Derek Hitchins; Lulu; 2010; {{ISBN|9781445751658}}; pp. 83β84</ref> Unfinished casing blocks of the pyramids of [[Pyramid of Menkaure|Menkaure]] and [[Pyramid G1-c|Henutsen]] at Giza suggest that the front faces were smoothed only after the stones were laid, with chiselled seams marking correct positioning and where the superfluous rock would have to be trimmed off.{{sfn|Lehner|1997|pp=212β213}} [[File:Great Pyramid Casing Stone Size Comparison.png|thumb|The size of a casing stone from the first layer (bottom) compared with one of the upper layers (top)]] The height of the horizontal layers is not uniform but varies considerably. The highest of the 203 remaining courses are towards the bottom, the first layer being the tallest at {{Convert|1.49|m|ft}}. Towards the top, layers tend to be only slightly over {{convert|1|royal cubit|m+ft|1|lk=in}} in height, with stones weighing around {{Convert|500|kg|lb}}.<ref>{{Cite journal |last=Lightbody |first=David Ian |date=2016 |title=Biography of a Great Pyramid Casing Stone |url=https://web.ujaen.es/investiga/egiptologia/journalarchitecture/downloads/JAEA1_Lightbody.pdf |journal=The Journal of Ancient Egyptian Architecture |volume=1 |pages=39β56}}</ref> An irregular pattern is noticeable when looking at the sizes in sequence, where layer height declines steadily only to rise sharply again.{{sfn|Petrie|1883|p=vii}}<ref>{{Cite book|last=Goyon|first=Georges|title=Les Rangs d'Assises de la Grande Pyramide|year=1978}}</ref><ref>{{Cite journal|last=Dash|first=Glen|title=The Curious Case of the Great Pyramid's Alternating Course Heights: An Unsolved Mystery|url=http://www.aeraweb.org/wp-content/uploads/2019/10/AG19_1.pdf |archive-url=https://web.archive.org/web/20191124143142/http://www.aeraweb.org/wp-content/uploads/2019/10/AG19_1.pdf |archive-date=2019-11-24 |url-status=live|journal=Aeragram|volume=19_1|pages=20}}</ref> So-called "backing stones" supported the casing, which were (unlike core blocks), precisely dressed as well and bound to the casing with mortar.<ref name="Fabric" /> Now, these stones give the structure its visible appearance, following the partial dismantling of the pyramid in the [[Middle Ages]]. Amidst earthquakes in northern Egypt, workers stripped away many of the outer casing stones,{{sfn|Tompkins|1978|p=17}} which were said to have been carted away by [[Bahri dynasty|Bahri Sultan]] An-Nasir Nasir-ad-Din al-Hasan in 1356 for use in nearby [[Cairo]].{{sfn|Petrie|1883|p=38}} 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. Today a few of the casing stones from the lowest course can be seen ''[[In situ conservation (archaeology)|in situ]]'' on each side, with the best preserved on the north below the entrances, excavated by Vyse in 1837. The mortar was chemically analyzed<ref>{{Cite book|last=Lucas|first=Alfred|title=Ancient Egyptian Mortars}}</ref> and contains organic inclusions (mostly charcoal), samples of which were radiocarbon dated to 2871β2604 BC.<ref>{{Cite journal|title=Radiocarbon Dates of Old and Middle Kingdom Monuments in Egypt|year=1995|doi=10.1017/S0033822200038558|last1=Bonani|first1=Georges|last2=Haas|first2=Herbert|last3=Hawass|first3=Zahi|last4=Lehner|first4=Mark|last5=Nakhla|first5=Shawki|last6=Nolan|first6=John|last7=Wenke|first7=Robert|last8=WΓΆlfli|first8=Willy|journal=Radiocarbon|volume=43|issue=3|pages=1297β1320|s2cid=58893491|doi-access=free}}</ref> It has been theorized that the mortar enabled the masons to set the stones exactly by providing a level bed.{{sfnp|Clarke|Engelbach|1991|pp=78β79}}{{sfnp|Stocks|2003|pp=182β183}} Although it has been suggested that some or all of the casing stones were made from a type of [[concrete]] that was cast in place, rather than quarried and moved, archaeological evidence and petrographic analysis indicate this was not the case.<ref>{{Cite book|last=Dipayan|first=Jana|url=https://www.researchgate.net/publication/288698728|title=Evidence from detailed petrographic examinations of casing stones from the great pyramid of khufu, a natural limestone from tura, and a man-made (Geopolymeric) limestone}}</ref> Petrie noted in 1880 the four sides of the pyramid to be "very distinctly hollowed" and that "each side has a sort of groove specially down the middle of the face", which he reasoned was a result of increased casing thickness in these areas.{{sfn|Petrie|1883|pp=43β44}} Under certain lighting conditions and with image enhancement the faces can appear to be split, leading to speculation that the pyramid had been intentionally constructed eight-sided.<ref>{{cite book |author=Lepre |first=J. P. |title=The Egyptian Pyramids: A Comprehensive, Illustrated Reference |year=1990 |page=66}}</ref><ref name=":0">{{Cite journal |last=Monnier |first=Franck |date=2022-06-25 |title=The so-called concave faces of the Great Pyramid: Facts and cognitive bias |url=https://journals.univie.ac.at/index.php/integ/article/view/6413 |journal=Interdisciplinary Egyptology |volume=1 |issue=1 |pages=1β19}}</ref> Laser scanning and [[Photogrammetry|photogrammetrical]] surveys concluded the concavities of the four sides to be the result of the removal of the casing stones, which damaged the underlying blocks that form the outer surface today.<ref>{{Cite book |url=https://www.researchgate.net/publication/228911535 |title=Combined High Resolution Laser Scanning and Photogrammetrical Documentation of the Pyramids at Giza |year=2005}}</ref><ref name=":0" />
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