Giza and the Stars: How did their knowledge of astronomy inform and influence Ancient Egyptian religious beliefs and pyramid building?
There exists a vast volume of work on how the pyramids and other monumental structures in Egypt were built by the Ancient Egyptians, as well as even some speculation on why they were constructed. This article looks at one of these speculative correlations in greater detail; that of how the ancient Egyptians’ understanding of the cosmos and its layout influenced the building, placement, and architecture of the pyramids and the religion practiced there. Through an examination first, of the religious beliefs and second, the archaeoastronomical work done by some leading modern scholars in conjunction with Ancient Egyptian writings, this article will show that the Ancient Egyptians utilised the cosmos for their religion and, by process of association, the alignment and construction of their pyramids.
The Pyramid Texts
The various monuments, temples, and other sacred buildings of Ancient Egypt contain copious amounts of writings. The walls of the buildings are covered in hieroglyphics, the tombs and sarcophagi inlayed with further inscriptions, and records made on papyri found throughout the remains of this once great civilisation. A portion of these texts are instructional guidance and protective spells to assist the deceased successfully navigate their way into the afterlife to become an akh in the celestial realm with the sun – god Re. These writings have become known as the Pyramid Texts; the Coffin Texts, and eventually the Book of the Dead are further developments of these instructions and spells made over time by the Egyptian priests.
Religious texts may be an appropriate starting place to examine whether the Ancient Egyptians utilised the cosmos to inform their religion and pyramid building. Egyptian religious beliefs indicate that the observation of stellar bodies in the heavens played a significant role in the afterlife. By way of example, an extract of one of these texts is provided here to showcase the belief system of the afterlife as it pertained to the cosmos.
You come in, you go out,
Your heart in joy at the praise of the lord of the gods;
A good burial after revered old age,
After old age has come.
You take your place in the lord-of-life,
You come to the earth in the tomb of the west.
To become indeed a living ba,
It shall thrive on bread, water and air;
To assume the form of phoenix, swallow,
Or falcon or heron, as you wish.
You cross in the ferry without being hindered,
You fare on the water’s flowing flood.
You come to life a second time,
Your ba shall not forsake your corpse.
Your ba is divine among the spirits,
The worthy bas converse with you.
You join them to receive what is given on earth,
You thrive on water,
You breathe air,
You drink as your heart desires,
Your eyes are given you to see,
Your ears to hear what is spoken;
Your mouth speaks, your feet walk,
Your hands, your arms have motion.
Your flesh is firm, your muscles are smooth,
You delight in all your limbs;
You count your members; all these, sound,
There is no fault in what is yours.
Your heart is yours in very truth,
You have your own, your former heart.
You rise to heaven, you open duat
In any shape that you desire.
You are summoned daily to Wen-nefer’s alter.
You receive the bread that comes before [him]
The offering to the lord of the sacred land.
The text above demonstrates that the Ancient Egyptians believed the stars were their end goal after this mortal life. The Egyptian belief that the sun disappeared in the west and then travelled through an underworld only to be reborn in the east each morning by the sky – goddess Nut was central to their cosmological belief system as well as their entire way of thinking. The belief that man passes through the same journey as the sun at night-time is referenced in the Pyramid Texts many times. Piankoff uses the examples of Pyramid Texts 1679 and 756 to showcase this. Respectively, they say that the dead man goes to the west of the sky and ‘He rests alive in the west, among the followers of Re, who present the road to the light’, and ‘Thou goest up towards thy mother Nut who seizes thy arm, she gives thee the roads [leading] towards the horizon, towards the place where is Re.’ Piankoff also states that due to the determinative in the Egyptian text in relation to the word ‘light’, that it is indicating that it is above the firmament, or otherwise, the stars. To put it another way that is clearer, ‘You will reach to the sky like Orion, your soul will be effective like Sothis.’ This is stating that the dead king will rise to the stars, just like the constellation Orion and the star Sothis.
The Stars as Gods
Thus far there has been a sampling of the religious texts as pertaining to the Ancient Egyptian belief system regarding their cosmological afterlife and their desire to unite with the stars. The question then arises as to why they would want to return to the stars in the first place? This is best answered by understanding that the Ancient Egyptians believed the stars to be their gods and the spirits of the dead, usually royalty but eventually everyone. Further, they also believed that in the region of the sky with the circumpolar stars, or the Imperishable Stars as they are often called by the Egyptians, was their version of heaven. They called this the Field of Reeds, or the Field of Offerings, among other names. Evidence of this can be found throughout the Pyramid Texts and other records. For example, the god Horus was identified as a god from early on in Egyptian ideology. There was a festival called the Festival of the Horus Star of the Gods, and royal domain names such as Horus the star of Souls, Horus Risen as a Star, and Horus, Star of the Corporation [of gods]. The clearest example of these names, however, would be Horus Star at the Front of the Sky.
Indeed Horus, Re, Isis, Osiris, and all the gods of Ancient Egypt were identified in the stars that were visible from the Giza plateau. Even the sky itself was the goddess Nut, and the earth was the god Geb. Together they bore Re, the sun-god, whom every night was consumed and travelled under the earth through the afterlife to be born again each morning by Nut. The Egyptians knew that the sun rose in the east and set in the west, but they placed vast significance on this act, enough to deify it and repeat it time and time again in their texts. The Egyptians saw the sun as the source of all life and happily greeted it, believing that at ‘night the earth is in darkness, as if it were dead, and thus the personification of the suns power’ became the sun – god Re.
Amongst their worship of the sun, sky and earth, the Ancient Egyptians also worshiped the stars. Horus was one of the foremost star gods of the Egyptians. In a Pyramid Text from Queen Neith’s pyramid we can read, ‘So, ascend to the sky amongst the stars in the sky, and those before you shall hide and those after you shall be afraid of you, because of this your identity of Horus of the Duat… of the one who strikes them, of the one who spews them out, and wipes them out, and you will strike them, spew them out, and wipe them out at the lake, at the Great Green. You shall come to stand at the fore of the Imperishable Stars and sit on your metal throne from which the dead are far away.’
Horus was represented in Egypt as a royal trinity through Horus the Falcon, Horus the King of Egypt, and the Heavenly Horus. The Ancient Egyptians faith in the eternal nature of their King and the astronomical observations and beliefs brought about this coupling. In fact, the religion surrounding Horus was able to be found in the sky in multiple places, not just the stars. In the story of Osiris, Horus suffered a wound to the eye. The Egyptians represented this wound and the successive restoration of Horus’ eye through the waning and waxing cycles of the moon, saying that the moon – god restored the eye each month. Further, the star Sirius, also known as the morning star, was thought of as a goddess and one that was associated with Horus in a solar aspect due to signalling the rising of the sun. How then do these religious beliefs of the Ancient Egyptians translate into a further knowledge of astronomy and then into the building of their pyramids? To answer that question, a further look into the astronomical knowledge and observations of the Ancient Egyptians is required.
Where was Horus?
There is much debate among modern scholars over what astronomical bodies should be attributed to which gods’ names as far as the Ancient Egyptians are concerned. This is not surprising considering the pantheon of deities that the Egyptians had. They seemed to have created gods for everything that they could observe in the sky, the earth, the water, as well as what they imagined existed, such as the underworld and afterlife. The Ancient Egyptians, like most ancient civilisations, attributed physical manifestations of these deities to what they observed. In order to ascertain what were the most probable stellar bodies that the Ancient Egyptians were using in their mythology and building, modern surveys, research, and theories will now be compared and contrasted with each other.
According to Krauss, the planet Venus, Orion, Sirius, and the Moon are found in literary descriptions in the Pyramid Texts. They are to be identified with Horus, Osiris, Isis, and Thoth respectively. Further, he identifies Seth with Mercury, pointing to the passages in the Pyramid Texts describing different interactions between Seth and Horus, and opines that they are dealing with the movements of Mercury and Venus in the Memphis skies of 2400 bc. There does appear to be some supporting evidence in the Pyramid Texts of the Pyramid of Unas for Krauss’ opinion that Horus was associated with Venus. In Utterance 294 line 437 it reads, ‘Unas has come out of this Dnj.t-jar after he has passed the night in his Dnj.t-jar. Unas appears in the morning.’ If Egypt had the same ‘morning star’ four thousand years ago that appears today, then Krauss would possibly be correct in assuming that Horus would be associated with Venus. Krauss appears to be mostly alone in his opinions of which stellar bodies should be attributed to which gods, however, as there is other contradictory evidence that supports another choice. He also admits to not being able to attribute Jupiter or Saturn to anything in the texts, which seems strange given that both are brighter than Mercury, and the other contemporary ancient cultures focused on them heavily. It is entirely possible that viewing angles for Egypt in the mid-twenty-fourth century bc were such that Jupiter and Saturn were not as prominent in the sky, or were diminished in intensity and not as bright, but there was no evidence supporting this possibility found.
Krauss does have a compatriot believer that Horus was Venus in Faulkner, though. Faulkner believes that the Morning Star and the Lone Star are both the same star, namely the planet Venus. He uses the fact that Venus can be seen when no other stars can be, and that it can be seen at dawn and at sunset as the reasoning behind his justification for this claim. Further, Faulkner dismisses that the Pyramid texts state that the Lone Star ascends from the eastern side of the sky and says that the expression is used so often that they probably just put it in out of habit. He goes on to state that there could be a case for the star being Jupiter, but that is the only other candidate, and not likely as it is less bright. He makes no mention of Mars as an option, which appears to be a more likely candidate when considering some of the ancient parallels in other cultures.
Using Horus as an example, some of the modern interpretations of stellar assignments such as those made by Faulkner and Krauss can be compared for feasibility and coherence. Anthes, for example, opines that the Heavenly Horus was a star, the sun, and possibly even the moon as well, with the opinion that this was because those astronomical bodies were the most prominent in the sky at their respective times. This is problematic as it indicates that the Egyptians were indecisive in their definitions of their own gods and religion. For a culture to build monuments and structures such as the Sphynx, the Great Pyramids, and others to the gods, and to do so with such a great level of skill and detail, and indeed are renowned for their adherence to detail and observation of the natural world, it just does not seem copasetic that they would be so either unspecific or undecided as to what was representing Horus.
To shed further light on the subject of Horus, a comparison of the Horus cult and that of Nergal, the Babylonian god, will show that there are many similarities between the two, and this proves important in assigning Horus a stellar body. The Babylonians assigned Nergal the planet Mars in the heavens as their physical manifestation of the god. The similarities continue when looking at the fact that both Horus and Nergal were warriors. Mars was also the God of War for the Romans, and there can be speculation as to whether or not the Romans just adopted this belief from their neighbours, or whether there was some significant event in the ancient past that happened that has somehow become associated with that planet as seen in the night sky as relating to war or destruction. Continuing the comparison with Nergal, he was associated with a mountain and the sunrise, as can be evidenced in a Sumerian hymn that says Nergal ‘rises in the mountain where the sun rises.’ This is in line still with the Ancient Egyptian belief of Horus of the Horizon, which is related to the mountain from which Re comes each dawn. Thus, it would appear safe to dismiss what Krauss has stated about the placement of Horus with Venus and place him instead as Mars in the sky. From this point, other celestial bodies can begin to be placed to form an accurate image of what the Ancient Egyptians were looking at when deciding what to, where to, and why to build.
Other Stellar Placements
There is a group of stellar bodies referenced throughout the Ancient Egyptian’s religion and texts as the Imperishable Stars, the Unwearying Stars, or the Stars that Know No Destruction. These stars are always visible in the Egyptian sky, as they are close to the stellar pole. As such, they occupy a smaller orbit and seem to just rotate in place as opposed to the rest of the stars which appear to track across the sky. These are called circumpolar stars, and because of their unique properties of not setting, they were symbolised by the Ancient Egyptians as being eternal. In Utterance 302 from the pyramid of Unas we can read the following:
Serene(?) is the sky, Soped lives (i.e., shines), for it is Unas indeed who is the living (star), the son of Sothis.
The Two Enneads have purified (themselves) for him as Meskhetiu (Great Bear), the Imperishable Stars.
The House of Unas which is in the sky will not perish,
The throne of Unas which is on earth will not be destroyed.
The humans (rm.tjw) hide themselves, the gods fly up,
Sothis has let Unas fly towards Heaven amongst his brothers the gods.
It is through these circumpolar stars and other constellations that the Ancient Egyptians identified and watched, and in some cases worshiped, that the inspiration for the building of the monuments came from, especially that of the king as associated with the gods and stars. Faulkner, in his translation of some of the pyramid texts, made note specifically of where the king was to be going to or interacting with the different stars and constellations. The most relevant of these to this analysis of Ancient Egyptian archaeoastronomy as pertaining to the pyramid building are reproduced here:
In your name of Dweller in Orion, with your season in the sky and your season on earth – said of Osiris and the dead King. #186
O King you are this great star, the companion of Orion who traverses the sky with Orion, who navigates the De’et with Osiris; you ascend from the eastern side of the sky, being renewed at your due season and rejuvenated at your due time; Nut has borne you with Orion, Year has put a fillet on you with Osiris. # 882-83
May Orion give him (the King) his arm, for Sothis has taken his hand. # 1561
[Speaking of Re and the King] His brother is Orion, his sister is Sothis.
These lines are important in attempting to plot out the exact location of the stars that the Ancient Egyptians were looking at. In doing so, it will create a scene of the night sky as seen by the Ancient Egyptians, and help to show why the pyramids were built where and how they were. Indeed, it is as Frankfort et.al. stated, ‘The ancient Egyptian left us no single formulation of his ideas which we may use as nuclear material; when we pick and choose scraps of ideas from scattered sources, we are gratifying our modern craving for a single integrated system. That is, our modern desire to capture a single picture is photographic and static, whereas the ancient Egyptians picture was cinematic and fluid.’ Through the efforts of many modern scholars, however, we have more than one ‘single integrated system’ to choose from when considering the building of the pyramids.
Monuments According To The Stars
Construction of a Pyramid
The Great Pyramid, otherwise known as the Pyramid of Khufu or Cheops, is the last standing remnant of the seven wonders of the ancient world. This is a great and significant achievement as it is a testament to how well-built this structure is in order to have withstood the forces of man and nature for almost four-and-a-half thousand years. This pyramid is situated approximately sixteen kilometres west of Cairo in the Giza plain on the western side of the Nile. Its base covers thirteen acres and it rises in two hundred and one stepped tiers. These tiers are made up of over two million pieces of limestone and granite, with an average weight of two-to-three tons each.
Fernie refers to Charles Smyth and his work on the measurements of the Great Pyramid in the eighteen hundreds. Smyth found that the slope of the Pyramid is close to the ratio 10:9, and that its height (484.9 ft), when multiplied by 109 equalled 91,840,000 miles, which coincidentally is close to the actual distance between the Earth and the Sun. Smyth believed that this meant that the pyramid builders must have known this distance. This is an interesting concept, and one that is shared by many people; academic, New Age metaphysicists, and conspiracy theorists to name a few.
Unfortunately, with the information and hard evidence that modern scholarship currently possess, it is not possible to come to a definite conclusion as to whether the distance from the Earth to the Sun was actually known by the ancient Egyptians. It would not be surprising to learn that they did know the distance, as they have proven that they were exceptionally skilled at observing the natural world, the sky, and were obviously great engineers, which by default requires exceptional mathematical skill and would go hand in hand with being able to determine the distance from themselves to their great solar disk. Interestingly, Smyth was not the only one to find interesting mathematical insights in the slope of the Great Pyramid, either. Magdolen purposes that the Ancient Egyptians discovered the ‘sacred pyramid’ before the Greeks by way of observing the sun’s rays and the corresponding shadows on a vertical pole through an act he refers to as solar geometry.
It appears the Ancient Egyptians wanted this structure to last forever, and thus far it has done that quite well, but why did they want this structure to last forever? As discussed in the previous sections, the Ancient Egyptians believed that their kings were eternal, and that when they died they journeyed to the stars to join their gods. However, their physical bodies needed a place of safety and protection while here on earth, and this is where the pyramids come in. The current accepted modern scholarship on the reason for the pyramids being built was that they were tombs for the king and his family to house their bodies in the aforementioned safety here on earth while their spirits travelled to the afterlife. This is why the walls are covered in the pyramid texts, which also as previously mentioned, are instructions on how to navigate the path of the afterlife as well as protective spells to keep the bodies safe. The building of these pyramids, then, was done in such a manner as to reflect the belief in the eternal nature of the spirit according to the Ancient Egyptians religion according to the stars. Unsurprisingly, they even used the stars that they held so important to help guide in the construction of the pyramids.
Most academics believe that there was a method of stellar alignment used in building the pyramids; most probably the circumpolar stars, or the Imperishable Stars as the Egyptians called them. This is a logical choice not only in the fact that the circumpolar stars appear ‘set’ in a location and just seem to rotate around one point, but, as discussed previously, due to this nature they were held as sacred to the Egyptians and perceived as the location that the deceased kings would travel to.
The Pyramid of Khufu is perhaps the best example of the exceptional alignment that the Egyptians achieved. The sides of this pyramid only deviate from a true north alignment by less than three arcminutes on average. Spence believes that it is logical to see through her experimental work that the pyramids were built according to an astronomical method, given that they are so well aligned and that the alignment gets more accurate as time progresses until the culmination at the construction of the Pyramid of Khufu, and then the alignments begin to shift away from true north in the opposite direction as would be the case when precession is taken into account. The method of orientation that Spence offers is that the pole was considered to be located on an invisible chord linking two circumpolar stars on opposite sides of the pole. These two stars rotate around the pole, and when they are vertically aligned above the north horizon (one at its upper culmination and one at its lower) an alignment made toward these stars with a plumb-line will be exactly oriented to true north, as long as the chord itself passes precisely through the pole. This method will produce alignments that become increasingly inaccurate as a direct function of time, and therefore has the potential to correspond with the viewed results of the pyramids’ progressive deviation from true north.
In finding a star that works for alignment, Fernie speculates that Thuban might have been the closest marker, though it is quite dim, and due to the accuracy that the pyramids are aligned, presumes a more rigorous method than just one star for alignment must have been used. Fernie then refers to an unnamed recent analysis that shows that a line drawn between the circumpolar stars Mizar and Kochab would very nearly cross the pole, and that the pyramids themselves exhibit the slight deviation that would result from using these stars to determine true north. It would appear that Fernie is referencing the work done by Spence discussed above. It is interesting to note that neither Fernie nor Spence reference the potential of using Venus, Mars, or any other star previously discussed as correlating to a god such as Horus for the alignment of the pyramids, but use the circumpolar stars, which the Egyptians thought of as the destination of the dead. This would seem a fitting location to align to if the pyramid was built to help the deceased navigate the afterlife.
Both accredited scholarship and pseudo-historians have looked to the pyramids of Ancient Egypt to see if their construction, architecture, or placement could signify something greater than just large, stone monuments. In this modern age of the internet, there is no shortage of theories on who built the pyramids, from thousands of slaves to extra-terrestrials. The fact that the pyramids were inexplicably and remarkably well-aligned to the cardinal points however, is one thing that can be agreed upon, if not the method in which it was achieved or the purpose for which it was done. It would seem apparent that the Ancient Egyptians felt so strongly about their relationship to the stars that it permeated their everyday lives in the form of their religion, their monument and tomb building, and their perception of the hereafter. Indeed, what better way to construct a pyramid that was purpose built to ensure safe travel to the afterlife, than with the stars that inspired the belief in the first place.
A. Piankoff, ‘The Sky-Goddess Nut and the Night Journey of the Sun’, JEA 20 (1934), 57 – 61.
A. W. Sjoberg, E. Bergmann, G. B. Gragg, and Enheduanna, The Collection of the Sumerian Temple Hymns, (J. J. Augustin, University of Virginia, 1969).
D. Brown, Mesopotamian Planetary Astronomy-Astrology, (Brill, 2000).
D. Katz, The Image of the Netherworld in the Sumerian Sources, (Capital Decisions Ltd, Bethesda MD, 2003).
D. Magdolen, ‘The Solar Origin of the “Sacred Triangle” in Ancient Egypt?’, Studien zur Altagyptischen Kultur 28, (2000), 207 – 217.
E. Hornung, Idea into Image: Essays on Ancient Egyptian Thought Trans. E. Bredeck (Timken Publishing, 1992).
H. H. A. Frankfort, J. A. Wilson, and T. Jacobsen, ‘Ch. 2 Egypt: The Nature of the Universe’, Before Philosophy: The Intellectual Adventure of Ancient Man (Penguin Books, 1968) 43 – 57.
J. D. Fernie, ‘Marginalia: Astronomy and the Great Pyramid’, American Scientist 92:5 (2004), 406 – 409.
J. P. Allen, ‘The Ancient Egyptian Pyramid Texts’, Writings from the Ancient World 23, (Society of Biblical Literature, Leiden: Brill, 2005).
K. Spence, ‘Ancient Egyptian chronology and the astronomical orientation of pyramids’, Nature 408, (2000), 320 – 324.
O. Neugebauer and R. A. Parker, Egyptian Astronomical Texts, Vol III, (London, 1969).
Pyramid Text, Utterance 294, Line 437 (E. Wall of the Antechamber), (http://www.pyramidtextsonline.com/translation.html#anteeast) Accessed on 25 September 2012
Pyramid Text, Utterance 302, (N. Wall of the Antechamber), (http://www.pyramidtextsonline.com/translation.html#antenorth) Accessed on 25 September 2012
R. Anthes, ‘Egyptian Theology in the Third Millennium B. C.’, JNES 18:3 (1959), 169 – 212.
R. Krauss, Astronomische Konzepte und Jeneitsvorstellungen in den Pyramidentexten, (Harrassowitz, 1997), 292.
R. O. Faulkner, ‘The King and the Star – Religion in the Pyramid Texts’, JNES 25:3, (1966), 153 – 161.
S. D'Auria, P. Lacovara, and C. H. Roehrig, 'Funerary Mythology', Mummies and Magic: The Funerary Arts of Ancient Egypt, Museum of Fine Arts (Boston, 1988), 27 - 37.
S. N. Kramer, R. Anthes, et. al., ‘Mythologies in Ancient Egypt’, Mythologies of the Ancient World (Double Day, Garden City NY, 1961), 85 – 86.
 An effective or positive spirit.
 The spirit.
S. D'Auria, P. Lacovara, and C. H. Roehrig, 'Funerary Mythology', Mummies and Magic: The Funerary Arts of Ancient Egypt, Museum of Fine Arts (Boston, 1988) 28—29.
 From the tomb of Paheri in el-Kab.
 D’Auria, et. al., Mummies and Magic, 32
 A. Piankoff, ‘The Sky-Goddess Nut and the Night Journey of the Sun’, JEA 20 (1934), 58.
 The King.
 R. O. Faulkner, ‘The King and the Star – Religion in the Pyramid Texts’, JNES 25:3, (1966), 158.
 H. H. A. Frankfort, J. A. Wilson, and T. Jacobsen, ‘Ch. 2 Egypt: The Nature of the Universe’, Before Philosophy: The Intellectual Adventure of Ancient Man (Penguin Books, 1968), 57.
 E. Hornung, Idea into Image: Essays on Ancient Egyptian Thought Trans. E. Bredeck (Timken Publishing, 1992) 158, 121-122.
 Painkoff, JEA 20, 57.
 Frankfort, et. al., Before Philosophy, 43.
 J. P. Allen, ‘The Ancient Egyptian Pyramid Texts’, Writings from the Ancient World 23, (Society of Biblical Literature, Leiden: Brill, 2005), 323.
 S. N. Kramer, R. Anthes, et. al., ‘Mythologies in Ancient Egypt’, Mythologies of the Ancient World (Double Day, Garden City NY, 1961), 85 – 86.
 Frankfort, et. al., Before Philosophy, 56.
 Allen, The Ancient Egyptian Pyramid Texts, 441.
 Pyramid Text, Utterance 294, Line 437 (E. Wall of the Antechamber), (Pyramid Texts Online) (http://www.pyramidtextsonline.com/translation.html#anteeast).
 R. Krauss, Astronomische Konzepte und Jeneitsvorstellungen in den Pyramidentexten, (Harrassowitz, 1997), 292.
 Faulkner, JNES 25:3, 161.
 R. Anthes, ‘Egyptian Theology in the Third Millennium B. C.’, JNES 18:3 (1959), 171.
 D. Brown, Mesopotamian Planetary Astronomy-Astrology, (Brill, 2000), 56.
 D. Katz, The Image of the Netherworld in the Sumerian Sources, (Capital Decisions Ltd, Bethesda MD, 2003. 404.
 A. W. Sjoberg, E. Bergmann, G. B. Gragg, and Enheduanna, The Collection of the Sumerian Temple Hymns, (J. J. Augustin, University of Virginia, 1969), 106.
 O. Neugebauer and R. A. Parker, Egyptian Astronomical Texts, Vol III, (London, 1969), 179.
 Frankfort, et. al., Before Philosophy, 56.
 Pyramid Text, Utterance 302 (N. Wall of the Antechamber), (http://www.pyramidtextsonline.com/translation.html#antenorth).
 Faulkner, JNES 25:3, 158, 160-161.
Frankfort, et. al., Before Philosophy, 53.
 J. D. Fernie, ‘Marginalia: Astronomy and the Great Pyramid’, American Scientist 92:5 (2004), 406.
 Ibid, p. 408.
 The Pathagorean Triangle, which has a ratio of 3:4:5, creating a right angle where the two shorter sides meet
 Called a gnomon.
 D. Magdolen, ‘The Solar Origin of the “Sacred Triangle” in Ancient Egypt?’, Studien zur Altagyptischen Kultur 28, (2000), 209.
 K. Spence, ‘Ancient Egyptian chronology and the astronomical orientation of pyramids’, Nature 408, (2000), 321.
Fernie, AS 92:5, 408.
 A unit of angular distance equal to a 60th of a degree.
 Spence, Nature, 320.
 The slow movement of the axis of a spinning body around another axis due to a torque (such as gravitational influence) acting to change the direction of the first axis. In this case, the earth's axis slowly changes pitch over time and causes the stars to appear in a different location in the sky in a cyclical patterm over a period of 26,000 years per cycle.
 Spence, Nature, 320.
 Ibid, p. 322
 Fernie, AS 92:5, 408.
 Further evidence that Fernie is referencing Spence’s work comes on p. 409 where he reproduces a graph plotting the orientation of the eight pyramids (Medium, Bent Pyramid, Red Pyramid, Khufu, Khafre, Menkaure, Sahure, and Neferirkare) that Spence had in her article.