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==== 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 minutes, 9 seconds off due east–west. Employing a pinhole produced much more accurate results (19 arc seconds off), whereas using an angled block as a shadow definer was less accurate (3′ 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 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>
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