Star in the Akhet

Star in the Akhet  

"For both the archaeologist and the native dweller, the landscape tells - or rather is - a story.  It enfolds the lives and times of predecessors who, over the generations, have moved around in it and played their part in its formation.  To perceive the landscape is therefore to carry out an act of remembrance, and remembering is not so much a matter of calling up an internal image, stored in the mind, as of engaging perceptually with an environment that is in itself pregnant with the past.  (Ingold 1993: 153)

“Now it is maintained by the Egyptians that it was they who first discovered writing and the observation of the stars, who also discovered the basic principles of geometry and most of the arts, and established the best laws.”  Diodorus Siculus, 'Library of History'  Book I, Chap. 69 (Loeb Classical Library edition Vol. 1, 1933: 239) 

Linear alignments between the royal mortuary complexes in the Ineb-hedj ('White Walls,' Gr. Memphis) necropolis and important sacred shrines at Iunu (Gr. Heliopolis) and Khem (Gr. Letopolis), were noticed from as early as the mid 19th century:

"In the early 1850's an Armenian engineer named Joseph Hekekyan conducted a series of test digs to a standard unparalleled in world archaeology prior to the Second World War, thanks to his surveying and recording of the different levels of finds.  The quality of his work can be set in context when we consider that a full 60 years later at Iunu even the great archaeologist Flinders Petrie recorded none of the stratigraphic information, and published no accurate general survey of the site (ill. 37).  Hekekyan carried out these works not to reconstruct the history of the ancient site, but to gather data on the geology of the Nile Valley, for an enthusiastic entrepreneur, Leonard Horner...........the original manuscripts, largely unpublished and housed in two separate institutions, the British Museum and the British Library.  These are now being brought back to life through the work of David Jeffreys, director of the Egypt Exploration Society archaeological operations at a second key ancient site, Mennefer (Memphis in the Greek texts), under and around the expanding modern village of Mit Rahina.  Hekekyan concentrated on the two ruinfields, Mit Rahina, ancient Memphis, and Matariya, ancient Iunu.  For both sites the contribution of the early recorder remains invaluable.  His work also opens up the question of the links between the two sites, one the centre of the sun cult, the other the node of government throughout ancient Egyptian history.  The importance of these links can be seen in the paragraph on the pyramid fields later in this chapter."  ('The Cult of Ra' Quirke, 2000: 74)

Hekekyan noted that Iunu is 45 degs. north east of Khufu’s pyramid, “…...clearly shown and specified on J. Hekekyan’s 1852 map of Heliopolis.” (D.G. Jeffreys 1998, 'The topography of Heliopolis and Memphis: some cognitive aspects', H Guksch & D Polz (eds), Stationen: Beitrage zur Kulturgeschichte Agyptens. Rainer Stadelmann Gewimdet, 63-71. Mainz.)

In 1874, C. Piazzi Smyth, the Astronomer Royal for Scotland, published, 'Our Inheritance in the Great Pyramid' that includes a map (Pl. V) of Lower Egypt, showing the 'Great Pyramid' at the southern apex of the Delta region quadrant.

'Our Inheritance in the Great Pyramid' C. Piazzi Smyth, 1877 (3rd edition): Plate XX

"With the general's glance of a Napoleon Bonaparte himself, his Academician savants in Egypt, in 1799, perceived how grand, thruthful, and effective a trigonometrical surveying signal the pointed shape of the Great Pyramid gratuitously presented them with; and they not only used it for that purpose, as it loomed far and wide over the country, but as a grander order of signal also, to mark the zero meridian of Longitude for all Egypt.  In coming to this conclusion, they could hardly but have perceived something of the peculiar position of the Great Pyramid at the southern apex of the Delta-land of Egypt; and recognised that the vertical plane of the pyramid's passages produced northward, passed through the northernmost point of Egypt's Mediterranean coast, besides forming the country's central and most commanding meridian line; while the N.E. and N.W. diagonals of the building similarly produced, enclosed the Delta's either side in a symmetrical and well-balanced manner.  But the first very particular publication on this branch of the subject was by Mr. Henry Mitchell, Chief Hydrogapher to the United States Coast Survey.  That gentleman, having been sent in 1866 to report on the progress of the Suez Canal, was much struck with the regularity of curvature along the whole of Egypt's northern coast.  To his mind, and by the light of his science, it was a splendid example on that very account, of a growing and advancing coast-line, developing in successive curves all struck one after the other from a certain point of physical origination.  And where was that physical centre of origin and formation?  With the curvature of the northern coast on a good map before him (see Fig. 1, Plate V.), Mr Mitchell sought, with variations of direction and radius, until he had got all the prominent coast points to be evenly swept by his arc; and then, looking to see where his centre was found it upon the Great Pyramid:  immediately deciding in his mind, "that the monument stands in a more important physical situation than any other building yet erected by man."  (Smyth 1874: 65-66)

In his book, 'Le Secret Des Batisseurs Des Grandes Pyramides' (1977: 90), Georges Goyon proposed that Khufu's pyramid aligned with Khem, 16.6 km to the north, using the North / Pole Star, Thuban.

Hans Goedicke, suggested the three royal pyramids at Giza were aligned with Iunu - possibly to the sanctuary of the ben-ben (Washington Post, 30.11.1983), and according to Mark Lehner and Miroslav Verner, the axes of the necropolises in Giza and Abusir were probably directed toward Iunu (Lehner 1985: 143; Verner 2001 (1997): 302-3)

"The pyramids at Abusir, just as at Giza, were not positioned in the cemeteries randomly, but in accordance with a particular scheme that is not yet understood in all its aspects. The fundamental axis of the cemetery at Giza was a line linking the southeast corners of the pyramids, while at Abusir it was a line linking the pyramid’s northwest corners. Both lines, the axes of the pyramid cemeteries at Giza and at Abusir, converge towards a point that lies at Matariya, an eastern suburb of modern Cairo. In ancient times this was the site of the temple of Re and the famous center of the sun cult, Iunu, in Greek Heliopolis. It is possible that this was the "fixed point" of the world of the pyramid-builders." (Verner 2002: 112-3)

note: the ancient Egyptians called the site of the Abusir necropolis, "Per Asir, ‘The Realm of Osiris"

Miroslav Bárta:  "As at Giza, the Abusir pyramids of Sahura, Neferirkara and Neferefra were very likely built (i.e. situated in the necropolis) according to a single master plan. Verner was able to show that their northwestern corners lie in a line which runs directly to the northeast and intersects the Giza pyramids line precisely at Heliopolis, in the sun temple of Ra (Verner 2002, 302––3)." Miroslav Bárta ('Location of the Old Kingdom Pyramids in Egypt', Cambridge Archaeological Journal 15.2 (2005: 186)

"It is therefore appropriate to ask, in a landscape as prospect-dominated as the Nile Valley, which sites and monuments were mutually intervisible and whether their respective locations, horizons and vistas are owed to something more than mere coincidence." (‘The Topography of Heliopolis and Memphis: Some Cognitive Aspects’ David Jeffreys)

"The idea that the distribution of the pyramids is governed by definable ideological (religious, astronomical, or similar) considerations is attractive. After all, if there were such reasons for the design of the pyramid and for the relationship of monuments at one site, why should we shut our eyes to the possibility that similar thinking was behind the apparently almost perverse scatter of the pyramids over the Memphite area? The argument that the Egyptians would not have been able to achieve this had they set their mind to it cannot be seriously entertained." (‘Discussions in Egyptology’ 30, Malek 1994: 101-114)

Bárta’s endorsement of the "single master plan" proposal that aligned the pyramid fields of Giza and Abusir with Iunu is assessed and developed here to gain more insights into the questions:  is it "more than mere coincidence", is it technically feasible, and which aspects of the royal afterlife beliefs can shed light on the "scheme that is not yet understood in all its aspects". The terrestrial, celestial and religious / cultural landscape of the ancient Egyptians in the Old Kingdom are all examined for clues that might shed light on the positional relationships of the royal mortuary complexes in the ‘White Walls’ necropolis.

The Abusir / Iunu alignment seems less convincing than Giza / Iunu. Perhaps it was of little consequence to the ancient Egyptians, but no direct line of sight to Iunu from the Abusir pyramid field existed - the layout of the pyramid field is also not as distinctive and coherent as at Giza.

The Giza / Iunu alignment proposed by Goedicke, Lehner, Verner and endorsed by Bárta also has a problem.  The alignment is based on the 'Giza diagonal' - a 1216 cubit (637m) long, straight line through the SE corners of the three pyramids aligned with Iunu to the northeast.

However, the three SE corners are not in a straight line.  A line between the SE corners of G1 and G3 misses the SE corner of G2 by 12m (39ft), and a line between the SE corners of G1 and G2, extended to G3, misses the SE corner of G3 by 23m (76ft) - either G2 is set back from the line about 12m (39ft), or G3 is offset to the east by 23m (76ft).

A line through the SE corners of G2 - G1 is ~44.6 degs E of N, and through the SE corners of G3 - G1, ~43.3 degs E of N (the corner (arris) angle of Khafra's pyramid was also 43.3 degs)

Dual diagonals at Giza

note:  G1 = Khufu's pyramid;  G2 = Khafra;  G3 = Menkaura;  DS = Sneferu's southern pyramid at Dahshur;  DN = Sneferu's northern pyramid at Dahshur.

1. a 2000 cubit long, 45 deg. diagonal, (link) from the centre of the east side of G1 to the centre of the west side of G3 (the extreme western and eastern limits of the group of three royal pyramids), defines the SW / NE axis of the Giza site layout  (the intersection of the 45 deg. diagonal with the SE / NW diagonal through the centre of G2, lies midway between the centre of the north side of G3 and the centre of the south side of G1).

2. a 2000 cubit, 45 deg. diagonal, offset to the east, with the SW end moved to the centre of G3 has the NE end at the entrance to Khufu's cult complex on the EW centre axis.

Khufu's mortuary complex was named Khufu's Akhet - often translated, 'Horizon of Khufu'.  The Akhet (Axt) was “the place of becoming Akh, the latter half of the Duat, lying between the Duat’s center, where the Sun unites with Osiris in the middle of the night, and the visible horizon, above which the Sun rises at dawn.” (J.P. Allen, 2005: 425).  Khufu's cult complex on the east side of the pyramid, was the active hub of his mortuary complex - produce from his many agricultural estates supplying his mortuary cult, were received at this pivotal intersection.  From here alignments radiate out to two important sacred shrines, and to the pyramids of three kings, all members of Khufu's family - Khafra, Menkaura, and Djedefra.

Similar "ray-like projections" radiating out from the royal tomb at Amarna, to various stelae and sanctuaries / temples, have been examined by Michael Mallinson. (Museum of Fine Arts, Boston, ‘The Sacred Landscape’ in ‘Pharaohs of the Sun’, 1999: 72).

Four alignments radiating out from Khufu’s Akhet:

1. Iunu (iwnw, 'pillars'), 45 degs NE

2. Khem (xm), 90 degs due north

3. the pyramid of Khufu's son and successor, Djedefra, 45 degs NW - mirrors the 45 deg NE Giza / Iunu alignment

4. the pyramids of another of Khufu's sons, Khafra, and a grandson, Menkaura, 45 degs SW along a 2000 cubit long diagonal, oriented 45 degs NE / 45 degs SW

1. Iunu, 45 degs to the NE

Map of Iunu showing temenos walls, mounds and obelisk, from 'Dawn of Astronomy' N.J. Lockyer 1894: 76

"At Heliopolis, as I have hinted, the matter is still less certain.  Almost every trace of the temple has disappeared, but of remains of temenos walls in 1844, when the site was studied by Lepsius, there were plenty............The walls at Heliopolis are the most extraordinary I have met with in Egypt, as may be gathered from the accompanying reduction of Lepsius' map.  The arrow in Lepsius' map is so wrongly placed that the plan is very misleading.  It follows from Captain Lyons' observations and my own that the longest mound heads 14 degs. N. of W. to 14 degs S. of E. within a degree; the condition of the mounds renders more accurate measures impossible.

note 1:  Since I left Egypt, in February, 1893, Captain Lyons has been good enough to comply with my request to repeat the observations.  I give the following extract from his letter:                                                                 South mound, old temenos wall, 289 1/2 degs mag. bearing = 19 1/2 degs N. of W                                           Wall at right angles to old temenos wall, 189 degs mag. bearing = 71 degs S. of W.                                             ...... the temple axis was directed 289 1/2 degs mag. bearing with corr. 5 1/2 degs = 284 degs = 14 degs N. of W. true amplitude."  (Lockyer 1894: 75-7)

note:  according to Lockyer / Lyon, the correction for true north from magnetic north was 5 1/2 degs W in 1893.

A dual linear alignment between Iunu and the royal mortuary complexes at Giza, may have something in common with a Dynasty 6 inscription that mentions Akhs and gods crossing over for their meals each morning and evening to Iunu:

"Any Akh or any god who will cross his arm against Pepi Neferkare when he goes up to the sky on the god’s ladder, the earth will not be hacked up for him, a deposited offering will not be laid down for him, he will not cross to the evening meal in Iunu, he will not cross to the morning meal in Iunu. N 428 (PM)  PT 478 §978-9

note:  Akhs (Axj) - the deceased, "whose ba has reunited with its ka, making possible eternal life as a spirit among the living." (J.P. Allen 2005: 425)

“Here are both the city Bubastus and the Bubastite Nome; and above it is the Heliopolite Nome. In this Nome is Heliupolis, which is situated upon a noteworthy mound; it contains the temple of Helios, and the ox Mneuïs, which is kept in a kind of sanctuary and is regarded among the inhabitants as god, as is Apis in Memphis. In front of the mound are lakes, which receive the overflow from the neighbouring canal. The city is now entirely deserted; it contains the ancient temple constructed in the Aegyptian manner, which affords many evidences of the madness and sacrilege of Cambyses, who partly by fire and partly by iron sought to outrage the temples, mutilating them and burning them on every side, just as he did with the obelisks. Two of these, which were not completely spoiled, were brought to Rome, but others are either still there or at Thebes, the present Diospolis - some still standing, thoroughly eaten by the fire, and others lying on the ground.” (‘Geography’ Strabo Book 17, Chap. 27)

“In Heliupolis I also saw large houses in which the priests lived; for it is said that this place in particular was in ancient times a settlement of priests who studied philosophy and astronomy; but both this organisation and its pursuits have now disappeared. At Heliupolis, in fact, no one was pointed out to me as presiding over such pursuits, but only those who performed the sacrifices and explained to strangers what pertained to the sacred rites. When Aelius Gallus the praefect sailed up into Aegypt, he was accompanied by a certain man from Alexandria, Chaeremon by name, who pretended to some knowledge of this kind, but was generally ridiculed as a boaster and ignoramus. However, at Heliupolis the houses of the priests and schools of Plato and Eudoxus were pointed out to us; for Eudoxus went up to that place with Plato, and they both passed thirteen years with the priests, as is stated by some writers; for since these priests excelled in their knowledge of the heavenly bodies, albeit secretive and slow to impart it, Plato and Eudoxus prevailed of them in time and by courting their favour to let them learn some of the principles of their doctrines; but the barbarians concealed most things. However, these men did teach them the fractions of the day and night which, running over and above the three hundred and sixty five days, fill out the time of the true year.   But at that time the true year was unknown among the Greeks, as also many other things, until the later astrologers learned from the men who had translated into Greek the records of the priests; and even to this day they learn their teachings, and likewise those of the Chaldaeans.”  (‘Geography’ Strabo Book 17, Chap. 29)

Iunu was an important religious centre with shrines and temples dedicated to many deities - fragments from a Dynasty 3 shrine, probably built during the reign of Netjerikhet, were discovered at Iunu.  Iunu is mention in a text on the outside of a Dynasty 3 beer jar that may have once held papyri - a summary of the contents written on the outside of the jar reads, "Year of: The Following of Horus;  11th occasion of the count of the herds of Iunu" (Strudwick 2005: 74)

Imhotep, who may have been responsible for the design of Netjerikhet's mortuary complex, held the title, ‘Great Seer’.  Rahotep, a probable son of Snefru, held the title, ‘Great Seer of Iunu' (wr mA iwnw) or possibly ‘Who sees / looks at the Great One of Iunu' (mAA.w wr iwnw).

The bas of Iunu (the 'deities of Iunu'), are mentioned in a year by year record of the Dynasty 5 kings, Userkaf, Sahura, and Neferikara.

A Coffin Text from the Middle Kingdom explains who the 'Bas of Iunu' are:  "I know the Bas of Iunu;  they are the Sun, Shu and Tefenut"  CT 154

In the New Kingdom 'chapter for opening the mouth of Ani' (Chap. 23), from the 'Book of Going Forth by Day', Ani identifies himself with 'Sah (sAH, 'Orion') the Great' who dwells with the 'Bas of Iunu'.

Iunu means 'pillar', and pillars are often mentioned in the Old Kingdom 'Pyramid Texts':

A royal epithet, 'Pillar of the Stars'* (iwn sbAw; Sethe Vol 1: 151; §280a) is found in the Dynasty 5 pyramid of Unis and the Dyn 6 pyramid of Teti.  In Teti's pyramid its written:  O28 (iwn) Z1 S29 (s) D58 (b) + the 'star' ideo. N14 (sbA) repeated three times + the 'divine' det. G7 (falcon on the standard).

Another royal epithet following 'the 'Pillar of the Stars'* is the celestial 'Pillar of Kenzet, the bull of the sky'* (Sethe Vol 1: 151  §280b)

*Faulkner note: 'the dead king'

O! your fields will pass away when the iAd-star is before me.  I am the Pillar of the Stars and they shall see me as the Pillar of Darkness (sic), the Bull of the sky, the Shining One, the Ox-herd who is on his pool...... CT 622

In Pepi 1 and Merenra's pyramids, the king acquired the sky, its pillars and its stars, and the gods came to him in obeisance........"Horus will lift Meryre, Seth will elevate him, and Pepi will make an offering outpouring and a star-outpouring." (P 449, M 360;  Sethe Vol 2: 139;  §1144b)

An epithet from the Old Kingdom reads: ‘Great pillar who causes his lands to live’ (iwn aA sanx tAwy.f) (JEA Vol. 92, 2006: 177)

An inscription from the TIP statue (BM EA 25) of a high priest of Memphis: "...that your ba go to heaven among the shining stars .... for the ka of the prince, protector of the Two Lands, foremost image of Memphis, stout pillar of great Iunu (iwn rwd n iwn wr)....."

A sculpture showing Ramesses II standing before Atum, and setting up 'the pillar (iwn) of the 'Bull of Iunu' for Atum, has a depiction of the pillar:

(Wainwright 1938: 107)

In the Dynasty 6 ‘Pyramid Texts’ of Teti and Pepi I, the king is the 'Bull of Iunu' (T 285 (P 372);  PT 408;  Sethe Vol 1: 393  §716e), and in Teti's pyramid also the 'Bull of Light' (Allen) or 'Bull of the Ennead' (Faulkner)  (T 286;  PT 409;  Sethe Vol 1: 393  §717a)

note:  N8 'sunlight' (wbn) is the determinative, but the word is 'Ennead' (psDt: Q3 (p) S29 (s) I10 (D) X1 (t) + 'sunlight' det. N8)

'Bull of Iunu'          'Bull of the Ennead / Light'

The Dynasty 5 king Unis was the 'big-faced bull' who came from Iunu, a wild bull of the savannah. (W 212)

Atum was the 'Father of the gods' (P 519; PT 577;  Sethe Vol 2: 323 §1521a) - the 'foremost' of the 'Big / Great Ennead' (pDt aAt) of Iunu, and genealogical father of the king through Osiris and Horus.  An inscription from the reign of Pepi I reads:  "The son of [Atum], 'Lord of Iunu' and of Hathor, mistress of Iunet (Dendera), Pepi....."  (Strudwick 2005: 93)

(earlier, in the Pyramid Texts of Unis and Teti, Sah (sAH, 'Orion') is 'Father of the Gods.'  W 180b (T); PT 274;  Sethe Vol 1: 213 §408c)

Atum (tm), 'Father of the Gods'        Sah (sAH, 'Orion') 'Father of the Gods'

Atum was also the king's father:  "Unis's father Atum will take the arm of Unis and allot Unis to those gods who are wise and experienced, the Imperishable Stars (ixnmw sk)."  (W176 (PM); PT 269; Sethe Vol 1: 198  §380b)

"Sah (sAH, 'Orion') has become encircled by the Duat, as the Living One (the sun) became clean in the Akhet;  Sopdet (spdt, 'Sirius') has become encircled by the Duat, as the Living One became clean in the Akhet:  This Unis has become encircled by the Duat, as the Living One became clean in the Akhet.  He has become akh for them, he has grown cool for them, inside the arms of his father, inside the arms of Atum."  W149 (TPMNNt);  PT 216;  Sethe Vol 1: 86 §151)

"Atum, put your arms around Pepi Neferkare as ka-arms, so that the ka of  Pepi Neferkare might be in it, firm for the course of eternity.  Ho, Atum!  May you extend protection over this Pepi Neferkare, over this his pyramid and this his work of Pepi Neferkare, and prevent anything bad from happening to it in the course of eternity, like you extended protection over Shu and Tefnut."  (N 359 (M); PT 600; Sethe Vol 1: 373  §1653)

"....with your father with Atum.......inside your fathers arms, inside Atum's arms........Atum, elevate him to you, encircle him inside your arms:  he is your son of your body, forever."  (W 155 (TPMNNt);  PT 222;  Sethe Vol 1: 122  §211c - 213)

"Ho, Horus!  This Pepi Neferkare is Osiris, this pyramid of Pepi Neferkare and this work are Osiris.  Betake yourself to him and don't be far from him in his identity of the pyramid."  N 359 (M); (PT 600; Sethe Vol 1: 375  §1657b)

"O, Big Ennead in Iunu!  You will make Pepi Neferkare be firm as you make this pyramid of Pepi Neferkare and this his work be firm for the course of eternity as the name of Atum, foremost of the Big Ennead, is firm."  (N 360 (PM); PT 601;  Sethe Vol 1: 377  §1660b)

Sah was also the king's father:  "Be alive!  Become young!  Be young! - at your father's fingers, at Sah's fingers, at the sky."  N 593 (PT 699)  Sethe Vol. 2: 529; §2180c

Iunu is probably the religious centre mentioned in Genesis 41:45

"Pharaoh gave Joseph the name Zaphenath Paneah.  He also gave him Asenath daughter of Potiphera, priest of On to be his wife."

And in Jeremiah 43:13

"He will demolish the sacred pillars (matstsebah) in the temple of the sun (Beyth Shemesh) in Egypt (Mitsrayim)

Stars / bas

The bas of Iunu laid down a stairway for the king to join with the above. (P 459)

Iunu was associated with stars - the ‘starry sky’ and the ‘Starry One’ (Osiris) were in Iunu:

"See, its starry sky (xA.s-bAs, lit. its 'thousand-are-her-souls') is in Iunu, the sun-folk are in Kheraha, because its thousand gods are born...."  CT 1030

According to Dynasty 6 Pyramid Texts, the bas of the kings appeared as stars.  From the pyramid of Pepi:  "You (Nut) have encircled the land and everything within your arms, and have placed this Pepi as an Imperishable Star that is in you (P 20)..........that you (Nut) might make (each of) them a star, as 'She of a Thousand Bas' (xA-bA.s), and they might not go away from you as stars, you should not let Pepi be away from you, in your identity of the above. P 22; PT 434 §785.  Allen's note on 'She of a Thousand Bas' (xA-bA.s): Nut, whose "Thousand Bas" are the stars of the night sky.

From the 'The Book of Going Forth by Day': "Behold the starry sky is in Iunu........." (Theban Recension, Chap. 136A)

To be spoken over a Sacred Bark, four cubits long made of pieces of malachite, and having upon it the tribunal of the nomes. There shall be made a sky with stars purified with natron and incense. Make an image of the Sun with ochre in a new bowl placed in front of this bark...... (Papyrus of Ani, Pl. 22, Chap. 133)

An Address to Osiris in Various Aspects: Hail to you (Osiris), Starry One in Iunu (Papyrus of Ani, Pl. 19, Chap. 15)  According to the earliest 'Pyramid Texts', Osiris was associated with Iunu (PT 219  §181)

The Big Enclosure

The 'Big Enclosure' (Hwt-aAt) at Iunu, was associated with 'Horus in the Big Enclosure' (Hrw m Hwt-aAt) an aspect of Horus, seen depicted as a falcon headed deity on a Dynasty 3 stela, embracing the Horus king Qahedjet (qA(i)-HDt, 'High is the White Crown').

Khufu was a traditional Horus king - the living embodiment of the god Horus, his Horus name, Horus Medjedju (Hrw mDdw), was adopted at his accession and subsequently used throughout his reign, and "used, for example, on royal decrees and in formal rock inscriptions in preference to the other names." (Strudwick 2005: 14)

An estate that served the royal funerary cult was named: 'Established is Khufu on the throne of Horus' (mn xwfw Hrw st Hrw).  The name of this estate clearly identifies Khufu as a traditional Horus king.

Khafkhufu was a priest of 'Horus, strong of arm' (Hrw qmA) or 'Horus with a raised arm'.

Nefri was the 'King's purificator of the pyramid Akhet Khufu' (wab nSwt Axt xwfw) and 'the one who sees Horus' (ie: the king) (mA Hrw / mAt j Hrw) (Abu-Bakr 1953: 46)

A son of Khufu, Hordedef (Hrw-dd=f), who was later renowned as a sage, has the name of the god Horus (Hrw) incorporated into his name.  His mastaba tomb (G 7210 - 7220) is next to the tomb of Khufu's eldest son, Kawab in the first row of double mastaba tombs in the Eastern Cemetery.

Horus titles held by members of Khufu's family, may refer to the reigning Horus king: 'Companion of Horus', beloved of him, 'Follower of Horus'; 'Beloved of Thoth and Horus'; 'Beholder of Horus and Seth'; 'Intimate of Horus' etc.

In the New Kingdom, the Sphinx was known as ‘Horus in the Akhet’ (Hrw m Axti, Gr. Harmakhis). This name is found much earlier in the Old Kingdom Dynasty 6 pyramid of Pepi Neferkare: "...This Pepi Neferkare has fallen on his side and Pepi Neferkare will stand up as a god, his control with him and his crown atop him like the Sun's crown when he emerges from the Akhet (Axt) and is greeted by Horus in the Akhet (Hrw m Axt)." N 412; PT 677 §2019c; Sethe Vol 2: 489.

This mention of ‘Horus in the Akhet’ in the Old Kingdom Pyramid Texts, suggests the New Kingdom name for the Sphinx may have something in common with the original Old Kingdom name, although ‘Horus in the Akhet' mentioned in PT 677 has the singular N18 determinative - in the NK its dual*. As all the kings who built at Giza were traditional Horus kings, a Horus name for the Sphinx is highly likely.

* "Axti is a nisbe from Axt, 'the Akhet'. In the New Kingdom this name is written G5 N19 A40, where Axti has been reinterpreted as a dual ('Horus of the Two Akhets')" (Allen 2005 (2000): 145)

The Sphinx with its human head wearing the royal nemes headcloth, may represent one of the kings - Khafra, the most likely candidate. Horus kings were identified with ‘Horus of the Akhet’ as in this inscription from the pyramid of Merenra:

"The living one, the living one of Horus's appearance, the Dual King, the living one of the Two Ladies' appearance, Merenre; the dual falcon of gold, Merenre; Nut's son of her belly, Merenre; Horus of the Akhet (Hrw Axti), lord of the sky (nb pt), Merenre, alive like the sun.........Horus of the Akhet, lord of the Akhet (nb Axt), Merenre, alive like the Sun. M 1b; PT 9 §7b; Sethe Vol 1: 4

The king in his afterlife also heard ‘cases’ as did Horus of the Akhet:

"When this time comes tomorrow, and the time of the third day (from now), and father Osiris Pepi is the sole star (sbA wati) in yonder eastern side of the sky, he will govern as a god and hear cases like Horus of the Akhet." P 529; PT 556 §1384a; Sethe Vol 2: 256

Atum was known as 'Lord of the Big Enclosure' (nb Hwt-aAt) - in the Coffin Texts Atum achieved eldership through his power when he fashioned Shu and Tefnut in Iunu.  (CT 80)

The Big Enclosure may also have been dedicated to at least four other deities, Shu, Tefnut, Geb, and Nut, who were the 'grandparents' / 'parents' of Horus and Seth (W 213).  Two pillars are mentioned in the inscriptions of Teti (T9; PT 324 §524), one of which was named Khnum (Xnmw).  Khufu's full name given to him at birth (probably by his parents Sneferu and Hetepheres), was Khnum-Khufu (Xnmw-xwfw) - if the 'Big Enclosure' existed already in Dynasty 4, Khnum's 'pillar' may have held a special significance for Khufu.  Khnum, the ram-headed deity of Aswan (Abw), ancient Egypt’s southern border town, was associated with royalty.  A relief block from Sahura's mortuary complex, shows the king being suckled by Nekhebet, accompanied by Khnum (ram-headed with the horizontal horns of the ovis longipes).  The text above Khnum reads: "he who dwells in the 'House of protection' the lord of Her-wer (Antinoe), he who dwells in the cataract city, lord of the house of Khnum."  Between both deities: "May all protection and life be around (literally behind) him, may he be healthy for ever." (Strudwick 2005: 85)

Khnum, 'He who dwells in the cataract city', has an interesting connection with Khnum-Khufu. Khufu's sarcophagus chamber was built of red granite, a prestigious stone, difficult to work, and came from Aswan, a considerable distance away.  The stone blocks may have been cut from the huge granite boulders found on the banks of the cataract - a subtle link with Khnum, the life giving waters of the river, and Khnum-Khufu's sarcophagus chamber.

Two enigmatic shafts are connected to the north and south walls of the chamber, and rise up through the superstructure of the pyramid as far as the outer face of the core masonry.

The purpose of these shafts is unknown.  It has been suggested they were 'ba-shafts', model passageways for the ba of the king to access specific areas of the sky.  'Ba-shafts', may have been inspired or were a subtle allusion to Khufu's full name, Khnum-Khufu (Xnmw xwfw)

Khnum (Xnmw) is written, W9 (Xnm) + E10 (a ram, bA).  Xnm can have a meaning of to join, unite with a god or the dead. (Faulkner 1962: 202), and ba (bA) was "the nonphysical essence of an individual or thing, the impression made on an observer;  akin to the modern notion of personality"  (Allen 2005: 426)

"The onomatopeic word for ram - ba, was similar to the spiritual aspect or ba of things" (R.H. Wilkinson 2003: 194).  In later times, Khnum was held to be the ba of the Sun, Osiris, and Geb.

An inscription in the antechamber of the pyramid of Unis, has Horus conducting the ka (kA) of Unis to his body at the 'Big Enclosure' in Iunu. (W 175), perhaps a part of the funerary rituals before the body of the dead king was placed in his pyramid.  The Dynasty 6 king Pepi, was the son of Khnum (P 472;  PT 524  §1238)

ben-ben

Goedicke suggested the three Giza pyramids were aligned to the sanctuary of the ben-ben.

A Benben Enclosure in Iunu, is mentioned in two Dynasty 6 pyramids:  "Atum Beetle! (itmw xprr) You became high as the hill; you rose as the benben in the Benben Enclosure in Iunu." N 359 (M 225); PT 600 §1652ab; Sethe Vol 1: 372

Atum rose (wbn, with bird det.) as a Benben (bnbn) The same bird sign begins the word bnbn, which has a determinative similar to M35, a 'heap of corn'. (M35 is the det. in wbn, 'overflow', pronounced the same as wbn, 'rise')

The bnbn is mentioned again in Neferkare's pyramid on the north wall of the antechamber: the benben (bnbn) is in Sokar's enclosure, the foreleg is in Anubis's house. N 519; PT 685 §2069a; Sethe Vol 2: 503 (Faulkner has bnbn-loaf (in the Mansion of Sokar)

A benu-bird in Iunu is mentioned in the ‘Book of going forth by Day’ (Papyrus of Ani) Chap. 17) :

"I know that Great God who is in it. Who is he? He is Osiris. Otherwise said: His name is the Sun, his name is 'Praise of the Sun', he is the ba of the Sun, with whom he himself copulated. I am that great Benu-bird in Iunu, the supervisor of what exists. Who is he? He is Osiris. As for what exists, that means his injury. Otherwise said: that means his corpse. Otherwise said: It means eternity and everlasting. As for eternity, it means daytime; as for everlasting, it means night."

The names of Osiris are the Sun (ra) and ‘Praise of the Sun’; Osiris is the ba of the Sun; Osiris is the Benu-bird.

"I am the Benu-bird, the ba of the Sun, who guides the gods to the Duat when they go forth." Pl. 32, Chap. 29B

"I am he who made his seat in Iunu (var. B3Bo: in the Mansion of the Pyramidion in Iunu; B4Bo: wbn ra wbnbn)) - four times - within the shining (wbnbn) Mansion of Sunrise (Hwt wbn ra) in Iunu, I am he who rises. I am he of the Pyramidion........" CT 422

"I have come from Khem to Iunu in order to inform the Benu-bird about the matters of the Duat."  ‘Book of going forth by Day’ (Theban Recension) Chap. 64)

The necropolis at Iunu 

Djedut, the necropolis at Iunu, was associated with royalty - "Teti cannot truly die, having become akh in the Akhet and stable (Ddti) in Djedut (Ddwt)."  T 187; PT 264 §350.

Pepi’s inscription reads: "You father Osiris Pepi! be akh in the Akhet and stable (Ddti) in the mound of Djedut (Ddwt).  P 339 (PT 487) Sethe Vol 2: 84; §1046b

"This Pepi has come to you, lord of the sky. This Pepi has come to, Osiris. This Pepi will wipe your face and clothe you with a god’s clothing, having become clean for you in Djedit." P 327; PT 477 §964

"In your (Osiris) identity of the one from Iunu, enduring in his necropolis......" W 152; PT 219 §181

note:  The bright star Alpha Centauri set 45 degs SW at the southwestern end of the 45 deg alignment between Iunu and Giza.

2. an alignment with Khem (xm; Gr. Letopolis), 90 degs due north

The ‘Horus of Khem’ shrine at Khem was an important shrine in the Old Kingdom.  Deep underground below Netjerikhet's pyramid and 'south tomb' are six panels showing Netjerikhet running or standing in various shrines. Netjerikhet is wearing the white crown of Upper Egypt in five of the panels, but under the 'South Tomb', a panel shows him wearing the red crown of Lower Egypt, standing in the Lower Egyptian shrine of 'Horus of Khem'. The 'Horus of Khem' shrine was obviously important to the king, as its the only Lower Egyptian shrine included on any of the panels.

The emblem of 'Horus of Khem' appears on the bracelets of one of the fragmentary high-relief statues of Khufu's father, Snefru, in his Lower Temple at Dahshur, and numerous elements from the insignia of 'Horus of Khem' were used in the decoration of the chest lid and walking stick of Khufu's mother, Hetepheres.

"Hr xm, 'Horus of Letopolis' ...... The god 'had important royal associations in the early Old Kingdom' (F.D. Friedman 1995: 36), various aspects of his insignia being depicted on the funerary furniture of Queen Hetep-heres." (T. Wilkinson 2001 (1999): 287)

"The title held by the High Priest of Horus of Letopolis (Khem), wnr, first appears at the end of the Third Dynasty (Goedicke, 1966)" (T. Wilkinson 2001 (1999): 273)

A great star was associated with Khem in a Middle Kingdom Coffin Text: my eyes are opened for me by the Eyeless One, the great star, joined to Khem, and I see with them. CT 106

Iunu and Khem are both on the same latitude - Iunu is due east of Khem, and Khem, due west of Iunu.  They are mentioned together in the Pyramid / Coffin texts, and in the 'Book of Going Forth by Day':

From the funerary texts of Pepi I: Live! Live - you have not really died - like Horus, Foremost of Khem, lives: he to whom the great cavern has been opened, the one of Iunu, he of the great baton, the great one of the sedan chair of Foremost of the Westerners. P 32

........who are in Iunu and Khem. CT 146

"I have come from Khem to Iunu in order to inform the Benu-bird about the matters of the Duat."  ‘Book of going forth by Day’ (Theban Recension) Chap. 64

Imseti, Hapi, Duamutef, and Qebehsenuef were the four children of Horus of Khem (PT 688 §2078-9)  The watchmen of Egypt, they fetched for the king his identity of an Imperishable Star.

Khem is due north of Khufu’s pyramid - a sighting to Thuban at its highest or lowest point in the sky as it closely circled the NCP could have been made to orientate the north / south axis of Khufu's pyramid.

Evidence of a sighting to Thuban is found inside Khufu's pyramid - two enigmatic shafts are connected to the sarcophagus chamber - the top end of the south shaft was facing an area of the sky where the distinctive 3-star asterism in the centre of Sah (sAH, 'Orion') appeared at its highest point in the sky due south c. 2570 BC, and the top end of the north shaft was facing an area of the sky where Thuban reached its highest point in the sky due north, again c. 2570 BC (Khufu's reign: 2589 - 2566 +-50 years).

A Dynasty 6 inscription from the pyramid of the Dual king Pepi Neferkare:  "Pepi has come to stand in the north of the sky and earth and Pepi has acquired the Two Lands like a king.  N 401; Sethe Vol I: 451;  §814bc

and, "....you will go on yonder path on which the gods go.  Turn yourself and see this serving that the king has made for you, that Foremost of the Westerners has made for you, that you might go to yonder gods, the northern Imperishable Stars."  P 37 (M 46); Sethe Vol I: 453-4;  §818

The dual shafts may have provided 'links' to both the north and south of the celestial realm for Khufu, the Dual king of the Two Lands.

In his 1981 paper, 'The Air-channels of Chephren's Pyramid', Dr Edwards wrote:  "....the channels were intended to serve as passages through which the spirit of the king could make its ascent to the astral regions....The Pyramid Texts frequently allude to the king's association in his afterlife with the stars and, in particular, with the circumpolar stars and with Orion and Sothis.  Scientific study has shown that at the time when the Great Pyramid was built, the northern channel, which sloped upwards at an angle of 31 degs with the horizontal, was in almost exact alignment with what was then the Pole Star (a Draconis), around which the circumpolar stars revolved, while three stars in Orion's belt passed each day at culmination directly over the southern channel, whose slope is 44.5 degs.  To suppose that such a setting of the channels had no magical significance seems highly improbable."  Edwards goes on to say that "the northern shaft "......was a substitute for the regular upward sloping corridor, a model representation of it, but no doubt considered equally effective as a magical element.  It was a simple solution, which not only satisfied the supposed requirements for the king's passage to the northern stars, but also made possible the introduction of a second channel as a means of approach to the constellation of Orion in the south, for which no special provision had previously been included in the architecture of a pyramid."

3. an alignment with the pyramid of Khufu's son and successor, Djedefra, 45 degs NW that mirrored the 45 deg NE Giza / Iunu alignment

The pyramid of Djedefra, son and successor of Khufu, was named ‘Djedefre is a sehed-star’ (Edwards), ‘Radjedef's star’ (J.P. Allen), 'Djedefre is a shining star' (Strudwick) - it had a similar angle of incline as his father’s pyramid - ~51.84 degs (sqd 5 ½).  Djedefra's pyramid is the most northerly of Egypt's pyramids, and was originally about the same size as Menkaura's pyramid.

The pyramid, ‘Djedefra is a shining star’ is 45 degs to the northwest from ‘Khufu’s Akhet’, and at 150m above sea level, the site had an unobstructed view to the SE, ideal for sighting to his father's mortuary complex. 

note:  the bright star Alpha Centauri, rose 45 degs SE when it was aligned with the pyramids of father, Khufu, and son, Djedefra whose pyramid was named 'Djedefre is a shining star' (Strudwick, 2005)

4. an alignment with the pyramids of another of Khufu's sons, Khafra, and a grandson, Menkaura, 45 degs to the SW along a 2000 cubit long ‘diagonal’ oriented 45 degs N of E / 45 degs S of W:

note:  Alpha Centauri, the same bright star that may have been used to set out the Khufu / Djedefra alignment could also have been used to set out the Khufu / Khafra / Menkaura alignment, but this time to Alpha Centauri setting 45 degs SW.

These four alignments radiating out from the centre of the east side of Khufu's pyramid may have something in common with an inscription from the pyramid of Pepi I:

"These four paths of yours are those which are in front of the tomb (HA.t, with jA, 'ascension', det.) of Horus, on which the god has walked since the going down of the Sun. (Sethe Vol 2: 244;  §1355ab).......the doors of the sky are opened for you....the doors of the tomb are opened for you, the doors of Nut are unbolted for you.....you ascend to the sky as a star, as the Morning Star"  (PT 553  §1366)

The god walked these four paths after sunset, in other words, at night, and the 'doors' of the tomb and the sky are plural.

An inscription from four Dyn 5 pyramids allude to the king's ba ascending along a path, through the doors of the sky, and into the company of the gods:

Faulkner: How good it is for those who see, how comforting it is for those who hear when Osiris the overseer of the gods arises! You have your tomb, O King, which belongs to the heart of Him whose seats are hidden; he opens for you the doors of the sky, he throws open for you the doors of the firmament(?), he makes a road for you that you may ascend by means of it into the company of the gods, you being alive in your bird shape. PT 667A §1943; Sethe Vol 2: 468

Allen: How beautiful to the sight, how satisfying to the hearing, is Osiris’s stance," is in the mouth of your tomb’s gods, Neith. He of the injured heart and inaccessible places shall open for you the sky’s doorway and pull open for you the Cool Water’s doorway. He shall make you a path, that you might emerge on it amongst the gods, alive in your ba. Nt 243 (P 279, M 199, N 340)

Also a later text from 'The Book of Going Forth by Day' (Theban Recension), Chap. 70:  ".....I travel around the sky on its four sides,....".

and from 'The Book of Going Forth by Day' (Papyrus of Ani, Pl 8, Chap 17):

"I go on the road which I know in front of the Island of the Just. What is it? It is Rastejau (r-sTAw, 'Mouth of the Ramp' - designation of the necropolis of Giza). The southern gate is in Naref, the northern gate is in the Mound of Osiris; as for the Island of the Just, it is Abydos (AbDw, burial site of the Early Dynastic kings). Otherwise said: it is the road on which my father Atum went when he proceeded to the 'Marsh / Field of Reeds' (sxt iArw - a region of the night sky, probably the region of the circumpolar stars). I arrive at the Island of the Horizon-dwellers, I go out from the holy gate. What is it? It is the 'Marsh / Field of Reeds', which produced the provisions for the gods who are round about the shrine. As for that holy gate, it is the gate of the Supports of Shu. Otherwise said: It is the gate of the Duat. Otherwise said: It is the door through which my father Atum passed when he proceeded to the eastern horizon of the sky."

The dead king was not simply lying dead in his tomb - he raised himself up and went to the sky as a star, as the morning god (P 526). He travelled around the southern and northern mounds (P 526; PT 553 §1364), and was taken to the god's places by those of the great ones (P 527) The king was ferried over to the eastern side of the sky, to where the gods were born - to where he was born. The king sat on his metal seat as the great one in Iunu (M 375). He searched for the endangered eye of Horus (T 181) - the bright eye of Horus was in Iunu (W 139). He was the 'Sole Star' in the eastern side of the sky, governing as a god, hearing cases like Horus of the Akhet (P 529) etc.

Ancient Egyptian measurements

“And Pythagoras learned from Egyptians his teachings about the gods, his geometrical propositions and theory of numbers, as well as the transmigration of the soul into every living thing.” ('Library of History' Diodorus Siculus Book I, Chap. 98)

“A second lawgiver, according to the Egyptians, was Sasychis,  a man of unusual understanding.  He made sundry additions to the existing laws and, in particular, laid down with the greatest precision the rites to be used in honouring the gods, and he was the inventor of geometry and taught his countrymen both to speculate about the stars and to observe them.” ('Library of History' Diodorus Siculus Book I, Chap. 94)

note:  Sasychis, is the Asychis of Herodotus, probably Shepseskaf, last king of Dynasty 4.

According to Petrie's survey, the length of the 'Giza diagonal' is 1047.4m.  Petrie concluded the length of the cubit used in Dyn 4...6 was 20.61"....20.65" (523.5mm.....524.5m).

(Petrie's survey estimates the length of a side of Menkaura's pyramid as 105.5m (201.5 cubits), but thought it most probable the sides were designed to be 200 cubits long (Petrie 1883: 204).  M&R thought that due to the lack of certainty for the exact length of the sides, 200 cubits was the most likely length. (Maragioglio & Rinaldi, Part 6, 1967: 96))

Apparent variations in the length of the cubit are evident from Petrie's survey data, but the variations are within building construction tolerances.  Apparent variations do not mean the AE had various standard lengths for the cubit - they simply show the builders were not working to engineering tolerances but to building construction tolerances where specified lengths realized on site can differ slightly from lengths specified by the architect.  The extent of the variations will depend on various factors - an intended 2 cubit wide passageway might be 2 cubits and a bit more or less depending on how good the builders were and the quality of the supervision.

Assuming a cubit of 523.7mm, the 1047.4m 'diagonal' is 2000 cubits long (523.7mm is the value of the cubit derived from Khufu's pyramid's survey data), and the angle, 45.1 degs E of N. This is to within a tenth of a degree, 45 degs (sqd 7). Taking into account the scale of the site (the 'diagonal' is over a kilometer long), if the 'diagonal' was intended, this degree of accuracy to a whole number seqed and 2000 cubits is a testimony to the surveyor's skill.  This SW / NE axis line may have determined the overall scale of the site, and defined the alignment with Iunu.

Four textual examples from the Old Kingdom, show that in these examples at least, designers specified measurements in whole numbers and multiples of 10, 100, 1000 cubits for primary large measurements used in architectural design. A walled estate of Metjen, a high official who died in the reign of Khufu's father, Sneferu, 200 x 200 cubits. The plan of the Dynasty 4 tomb of Debehen was designed with specified measurements of 100 x 50 cubits - a 1:2 rectangle.  A text from the Dynasty 5 Sun Temple of Niuserra mentions a stone structure with a length of 7000 cubits (Strudwick 2005: 90).  The ground plan for Izezi's Dynasty 5 Sed festival enclosure, 1000 x 440 cubits (Strudwick 2005: 313) - 1000 cubits is half the length of the 'Giza diagonal' and 440 cubits is the length of a base side of Khufu's pyramid.

Izezi's Sed festival enclosure is similar in size to the enclosures of the Dynasty 3 mortuary complexes of Netjerikhet and Sekhemkhet. The longest straight walls of Netjerikhet's stone walled rectangular enclosure, are 1000 cubits long (inside measurement).  Sekhemkhet's enclosure to the southwest is similar in size, and another enclosure further to the southwest is even larger.

Mastaba 17 at Maidum, is 200 x 100 cubits - a 1:2 rectangle (Petrie, Mackay, Wainwright 1910: 3). Khufu's sarcophagus chamber is 20 x 10 cubits - a 1:2 rectangle (an Early dynastic royal tomb about 2.4 km SSE from Khufu's pyramid had a similar size of burial chamber approx. 20.6 x 10.7 cubits with a wooden inner chamber built inside).

The ancient Egyptians specified linear measurements with cubits subdivided into palms and fingers.  That the division of the cubit into 7 palms and each palm divided into 4 fingers, was probably derived from the forearm, hand, and the four fingers of the hand, is indicated by the determinative for cubit (mH), D42, 'forearm with palm down'.  The 'palm' (Szp) unit was about 75 mm - approximately the width across the knuckles of the 4 fingers of the hand.  The ideogram for palm is D48, 'hand without thumb'.  Each 'finger' unit, about 19mm, was about the average width of a finger across the knuckle.  The 'finger' unit (Dba, 1/28th of a cubit) was written with the ideogram for 'finger', D50.

The signs used for cubit, palm and finger are all taken from the human forearm, hand and the four fingers of the hand, which makes it highly likely these units of length were derived from an idealized forearm / hand / finger.

The cubit and its sub-divisions may also be related to the lunar cycle - four phases of the moon were named by the ancient Egyptians - smdt (full moon, half month festival), snt (first quarter, 6th day festival), psDtyw (new moon), dnit (last quarter).

Month (Abd), was written with a combination of N11 (crescent moon) and N14 (five-pointed star), and 'half-month' with half crescent moon sign N11, and N14 (five-pointed star) - the rising of certain stars and the phases of the moon were both used for the timing of sacred rituals.

The 'palm' (Szp, 1/7th of a cubit) was also written simply with what appears to be N11, the 'crescent moon', an abbreviation of O42 (Szp) Q3 (p) + determinative N11 ('crescent moon').  The use of the crescent moon for 'palm' suggests an association with the lunar cycle.

The name of Thoth (DHwty) was written with the 'sacred ibis on standard' sign, G26.  The long curved beak of the ibis is reminiscent of the shape of the crescent moon.  Seshat the female scribe had a crescent moon-like symbol over her head as part of her headdress.  Both Thoth and Seshat had a role to play in the reconstitution of the king, with scribal tasks, numbering, timekeeping and building.  Both Thoth and Seshat are attested from the early dynastic period.

The common unit for linear measures of land was the khet (xt, 'rod', also called the 'rod of cord'), of 100 cubits.  (a setat (sTAt) was a square khet or 10,000 square cubits)

A much longer unit called a 'river-measure' (itrw) was 20000 cubits.

The 45 deg diagonal of a square defined an ancient Egyptian unit of length, the ‘double remen’ of 1.4 cubits (74 cm). "A double-remen was the length of the diagonal of a square whose side was one cubit.........It is thought that the double remen was used in measuring land, because it enabled areas to be halved or doubled without altering their shapes......a square on the side of the double-remen is double the area of a square on the cubit." (Gillings 1982 (1972): 208-9)

Area measurement was important in assessing grain production, taxation etc:

mH-tA = 100 square cubits;  sTAt = 10,000 square cubits (0.27 ha); xA-tA, lit.'thousand land', 1000 strips of 1 x 100 cubits) = 100,000 square cubits (2.74 ha).

Inscriptions in the Dynasty 3 tomb of Metjen, mention the standard measurement of area, the sTAt, in multiples of 200, 50, 20, 12, and 4 sTAt - at least by Dynasty 3, scribes were calculating areas.

Numbers used to specify the measurements of sacred buildings and other areas related to the king's afterlife were probably carefully chosen.  For example Horus's celestial boat was 770 cubits long, the equivalent of a modern day ocean going liner:

"Morning God (nTr dwA with 'star' det.), Horus of the Duat (Hrw dA.t), divine falcon, bee-eater (wAD(w)AD-bird) to whom the sky gave birth!.......You are ba and apparent at the fore of your raft (smH) of 770 cubits that the gods of Pe caulked for you, and the eastern gods bent into shape for you.  Let this Meryre proceed with you in your rafts cabin (Sna.w)."  (P 467 (MN);  PT 519 §1207-9)

Quirke on the Amduat:  "One of the most striking features of these accounts of the unknowable is the mathematical precision, both in the naming and in the actual measurements.  Thus the second and third hours specify the area covered as 309 iteru in length, and 120 in width." (Quirke 2000: 48)

309 iteru = 6180000 cubits (3236 km);  120 iteru = 2400000 cubits (1257 km)

309 iteru is about four times the distance from the southern border of ancient Egypt at Aswan to the northernmost tip of the Delta region.

In the Amduat, it is the length of the watery region Wer-en-es ('Land of Plenty')

12 x 3235.8 = 38830 km (equatorial cir. 40076 km;  polar cir. = 39940 km)

5 x 1256.640 km = 6283 km

Establishing long straight-line alignments is a straightforward procedure.  First the direction of the line is determined - in the case of the Giza / Iunu or Giza / Djedefra alignments, the diagonal of a square.  A square is created on the ground oriented to the cardinal points (the square base of Khufu's pyramid is one of the finest examples of the surveyors' skills in setting out a square on the ground, accurately aligned to the cardinal points). A backsight and foresight is set up with a plumb line at the SW and NE corners of the surveyors square. At night, either an appropriate rising or setting bright star and / or fire signals can be sighted to. During the day, a bright reflective surface reflecting the sun's rays or smoke signals can also be used.

Khem is due north of Khufu’s pyramid and the possible intended alignment between the 'Horus of Khem' shrine and Khufu's funerary complex, may have been determined by sighting to Thuban at its highest or lowest point in the sky as it closely circled the NCP.

Sighting to a bright star setting 45 deg SW was a useful aid in setting out the 2000 cubit long 45 deg ‘Giza diagonal’. The constellation ‘Crux’, in the form of a cross, set in the SW, and 80 minutes later, Alpha Centauri, the third brightest star in their sky after Sirius and Canopus, also set in the SW.

Alignments with Alpha Centauri are not possible today, as it is not visible from Giza - it remains hidden below the horizon, but when Khufu’s pyramid was at the design stage, c.2585 BC, Alpha Centauri rose 45 degs south of east, and set 45 degs south of west - a perfect bright point of light / star to sight to if an alignment with Iunu was intended.

note:  Alpha Centauri, the nearest star system to our solar system, is actually a triple-star system, the combined light of two of the stars appearing as a single bright source of light. Alpha Centauri A is the largest of the three stars and is slightly larger than our sun at 1.708 million kilometres in diameter (1.227 times the diameter of our sun). Alpha Centauri B is slightly smaller than our sun at 1.204 million kilometres in diameter (0.865 times the diameter of our sun). The third star, Proxima Centauri, is a much smaller ‘Red Dwarf’ star, about one seventh the size of our sun.

Our sun viewed from Alpha Centauri c.2850 BC, would have been seen as a 0.5 magnitude star near the constellation Cassiopeia. This same area of the sky when viewed from Giza, c.2585 BC, appeared over the NE horizon, 45 degs NE - directly in line with Iunu - from the perspective of Alpha Centauri - the ancient Egyptian sun rose above Iunu in line with Giza.  The Alpha Centauri triple-star system is highly rated as a potential star system for providing life conditions similar to our own solar system.

The three royal pyramids at Giza, and the important religious centre of Iunu, were all aligned either intentionally or unintentionally, with a bright star that is actually a three-star system, the third star, a ‘Red Dwarf’, considerably smaller than the other two.

The casing stones in Khufu's pyramid are white, fine-grained limestone, with very few fossil shells.  The first course of casing stones in Khafra's pyramid was made up of red and brown granite stones, but the main bulk of the pyramid was clad in light gray limestone, grayer, harder and more fragile than the casing stones of Khufu's pyramid.

The third pyramid at Giza is considerably smaller, and differs from the other two pyramids in that for about a quarter of its height (at least 16.4 m high, up to the 16th course) it was clad in red granite. Red granite was a prestigious stone, normally only used for special areas in the royal mortuary complexes - it was difficult to work, and came from a considerable distance away - from Abw, ancient Egypt’s southern border town. Casing the entire lower part of Menkaura’s pyramid with this expensive stone was unprecedented for a Dynasty 4 pyramid suggesting an important reason for its use - perhaps using a prestigious stone made up for the small size of the pyramid compared to the other two.

Khufu’s pyramid is 45 degs south of east from Djedefra’s mortuary complex, at Abu Rawash.  An observer at Djedefra’s funerary complex looking SE past Khufu’s pyramid, saw Alpha Centauri rising on the same sight line, 45 degs south of east.  (Simultaneously, the distinctive large constellation of Orion (sAH) was setting in the southwestern sky, and Canopus, the second brightest star in their sky was setting about 15 degs west of south)

At the beginning of Khufu's reign, Alpha Centauri rose 45 degs SE, and set 45 degs SW, and at its highest and brightest point due south, halfway between these rising and setting points, Alpha Centauri reached 22.5 degs altitude - half 45 degs.

The 45 deg angle (sqd 7) also appears in Khufu’s pyramid. The top section of the upper southern shaft has an angle of incline of 45 degs. This means the top end of the shaft was facing an area of the sky where the distinctive 3-star asterism in the centre of Orion reached at its highest in the sky due south when the pyramid was built.

Khufu’s father, Snefru, built two pyramids at Dahshur to the south of Giza. The northern pyramid at Dahshur was named: ‘the place of Snefru's appearance’ (Allen), 'Snefru Gleams' (Edwards); ‘The Shining Pyramid' (Baines & Malek).  The N28 ideogram used in the name can simply mean 'hill' (Faulkner 2002 (1962): 185), and is translated 'earth-hill' (Faulkner) or 'hill of land' (Allen) in PT 333 § 542a; Sethe Vol 1: 277). N28 has a phonetic value of xa - for example in the word 'approach'; 'appear in glory of god or king, especially of king's accession.

Ahmed Fakhry measured traces of the upper casing of the small pyramid south of Sneferu's southern pyramid, and concluded the pyramid had a probable angle of incline of 45 degs (sqd 7). ('The Monuments of Snefru at Dahshur' Vol 1, 1959: 94)  Petrie's earlier estimate was 44.57 deg.

Snefru’s northern pyramid had a probable intended angle of incline of about 45 degs (sqd 7), and this same 45 deg angle aligned the ‘Enclosure of Ptah’ in Ineb-hedi (‘the White Wall’, Gr. Memphis), with Snefru's pyramid, 45 degs to the SW.

"The city of Memphis which has now disappeared almost completely was the administrative and religious center of the 1st Lower Egyptian nome. It was the royal residence and capital of Egypt during the Early Dynastic Period and the Old Kingdom, and many later kings maintained a palace there. The city’s temples were among the most important in the land." (Baines & Malek 1986 (1984):134)

Alpha Centauri set 45 degs SW, which means it set behind Snefru’s northern pyramid viewed from any suitable viewing point along the 45 deg direction line linking his northern pyramid with Ineb-hedi (Gr. Memphis).

The two pyramids at Zawyet el-Aryan ('Unfinished' and 'Layer'), were also aligned 45 degs SE, with the ‘Enclosure of Ptah’ in Ineb-hedi. Alpha Centauri rose 45 degs SE which means both pyramids could have been aligned with Ineb-hedi using sightings to Alpha Centauri as it rose in the SE.  According to Edwards, the 'Unfinished pyramid' at Zawyet el-Aryan was named ‘Nebka is a star’.

An observer at Iunu looking towards the south western horizon saw Canopus, the second brightest star in their sky, setting about 15 degs west of south.  The sight line went between Sneferu's northern and southern pyramids at Dahshur.

(the lower part of Sneferu's southern pyramid at Dahshur has an angle of incline of about 54.46 degs (sqd 5).   A heading, 54.46 degs north of east from this pyramid, led to Ineb Hedi and beyond, to Arcturus, the forth brightest star in their sky, rising over the north eastern horizon)

Alpha Centauri was a useful aid for determining direction lines 45 degs SE and SW from c.2700 - c.2560 BC. This means that many of the early Dynasty 4 pyramids could have been aligned with significant sacred places and other pyramids built by members of the same family, using sightings to Alpha Centauri as it rose or set.

Alpha Centauri rising 45 degs SE:

‘Djedefra’s shining star’, aligned with 'Khufu’s Akhet' (G1)

‘Nebka is a star’ aligned with Ineb-hedi

Alpha Centauri setting 45 degs SW aligned with:

Ineb-hedi / Sneferu’s ‘shining pyramid’ (DN)

Iunu / ‘Khufu’s Akhet’ (G1), ‘Khafra’s great place’ (G2), ‘Menkaura’s divine place’ (G3)

Our present understanding of ancient Egyptian astronomical knowledge rules out any possibility the ancient Egyptians knew Alpha Centauri is a triple star system, but its quite possible rising and setting stars were used for establishing simple straight line alignments between sacred places and other royal mortuary complexes built by kings from the same extended family.

A major theme of the royal afterlife beliefs in the Old Kingdom 'Pyramid Texts', was the belief that stars were gods / akhs / bas. In the earliest 'Pyramid Texts' inscribed inside the Dynasty 5 pyramid of Unis, the king was born as a star and appeared as a star / god in the sky. In the earliest Pyramid Texts for example, Unis became clean in the cool water of the stars §138, the 'Imperishable Stars' raised Unis aloft §139, and Unis led the Imperishable Stars, §373. Unis was born as a star §262, and he appeared as a star §263. Unis parted his place in the sky among the stars of the sky, for he was the lone star at Nut's shoulder §251. Atum, the 'father' of Unis, alloted Unis to the wise and experienced gods, the Imperishable Stars §380. He was the son of Sopdet (spdt, personification of Sirius, the brightest star in their sky) §458, and was given title as greatest controlling power, by Sah (sAH, 'Orion'), the father of the gods (§408).

Horus, their sky deity and god of kingship had a stellar aspect to his multi faceted celestial persona.  Some examples of Early Dynastic seal impressions: 'Horus, star of the corporation' (Hrw-sbA-ht), Anedjib, Dyn 1; 'Horus risen as a star' (Hrw-h-sbA), Hetepsekhemwy, Dyn 2; 'Horus, the star of souls' (Hrw-sbA-bAw), Khasekhmwy, Dyn 2; 'Horus, the foremost star of the sky' (Hrw-sbA-hnti-pt), Netjerkhet, Dyn 3.

Horus, as 'Horus of the Duat' was also the 'Morning God / Star' the divine falcon (P 467; PT 519 §1207; Sethe Vol 2: 176). The 'Morning God' was a star: ".....as you go forth from here as a star, as the Morning God / Star. (N 411 (PT 676) Sethe Vol 2: 487; §2014b)

All the kings who built at Giza were traditional Horus kings with Horus names adopted at their accession.  Aligning to bright stars may have been a way of linking a kings mortuary complex with ‘Horus, risen as a star’ and / or his ancestors who appeared as stars in the sky.

Ancient Egyptian 5-rayed stars are very similar in appearance to starfish.  From the New Kingdom 'Book of Nut':  ".....Their evils fall to earth and the souls go forth which had fallen to [earth. Their tears drop becoming] fish. [The life of a star begins in the lake. It goes forth] from the [water]; it flies upwards, out of the sea and out of the (previous) form. It is the life of stars. They go forth from the Duat and they withdraw to the sky...." (EAT Vol. I, N&P 1960: 68)

The 'star' determinative sign was used for:  'praise god' (dwA nTr);  'praise' / 'worship' (dwA);  'morning' (dwAyt);  an adze for the 'opening the mouth' ritual named, 'the great one of the morning' (dwA-wr).  The nTrti-blades ('dual gods'), also used in the 'opening the mouth' ritual, were named sbAwi ('stars') in inventory texts from Neferirkare's Dyn 5 funerary complex.

The ancient Egyptian builders used a wooden frame in the form a capitol 'A', a 'square level', together with a plumb bob suspended from the apex of the A-frame to check the level of horizontal surfaces and establish equal levels (Arnold 1991: 13).  According to Faulkner, a 'sbA', written with a sign in the form of a capitol 'A' next to the star (sbA) sign, is a possible ancient Egyptian 'surveying instrument' (Faulkner 2002 (1962): 219).  This 'instrument' was written with the star sign, N14, that suggests its use may have involved stars.

From as early as the Old Kingdom, the ancient Egyptians were probably systematically observing stars. ‘Hour-stars’ or ‘time-marking stars’ are alluded to in the earliest Pyramid Texts: "O you in charge of the hour-stars, who precede the Sun...." (Sethe Vol 1: 145; §269a), and: "Now that Unis has swept away the night and Unis has sent off the hour-stars....." (Sethe Vol 1: 264; §515a)

‘Hour-stars’ (wnwt) is written with the star determinative, N14, repeated three times.

The importance of stars in the afterlife beliefs of the ancient Egyptians is evident from as far back as the pre / early dynastic period:

"As far as the afterlife was concerned, the loftiness of the pyramid hints at its celestial dimension.  The Pyramid Texts refer to a journey in the company of the sun and stars.  In particular, the king was believed to join the circumpolar stars which surround the Pole Star.......

A picture of a boat pecked into the northern rock face of the Wadi Abu Mu'awwad in the eastern desert has a star some distance above the prow.  "The technique and patination of the star and boat are identical, suggesting that both were made at the same time, as part of the same composition.  It looks very much as if the boat is following the star.  At another site in the eastern desert on the northern side of the Wadi Hammamat the largest and most impressive boat has a star above the prow of the boat.  "Here, and in the Wadi Abu Mu'awwad, there seems to have been no doubt in the minds of the ancient artists that the afterlife journey would be guided by a star.  Whether or not the stars were also believed to be the boat's ultimate destination, we can only guess;  but its a tempting possibility."  (T. Wilkinson, 2003: 158)

A pre / early dynastic knife handle (Metropolitan Museum 26.241.1), also shows a star above a boat carrying the king.

"A Predynastic palette from Girza shows a celestial cow goddess, her head surrounded by stars.  This object indicates that the worship of a female protective deity with astral connotations, perhaps already identified as Bat, was a feature of Egyptian religion from at least the middle of the forth millennium BC (Hornung 1983: 103)"  (T. Wilkinson 2001: 282)

A row of stars was used in a relief from a Dyn 2 temple dedicated to Hathor (lit. 'House / Enclosure of Horus')  The lower part shows a boat, and the upper part shows the king taking part in the foundation ceremony.

Measuring long distances is problematic, but they can be determined by using sight lines intersecting with each other at known angles, the distances calculated with simple geometry. If the Khet had the meaning of a 'rod of cord', this may be an indication their measuring cords were as long as 100 cubits (about 52m). Depending on the weather conditions, long cords can stretch or contract however, making consistent, accurate measurements difficult.

The 2000 cubit (200 khet) long 'Giza diagonal', extended 22 times its length (or 100 times the length of the 440 cubit long side of Khufu's pyramid) to 44000 cubits (440 khet), reaches Iunu to the northeast, where its aligned with the area of the main temple compounds (see Quirke 2000: 112 fig. 54 for map).

According to the EES Delta Survey data, the coordinates for Iunu are 30.125 N; 31.307 E, but its not possible to know the true extent of ancient Iunu, as it now lies under the Matariya district of Cairo - the only surviving obelisk (Google Earth (GE) coordinates: 30.129350 N 31.307500 E) dates from the Middle Kingdom, Dynasty 12, Senwosret.

The Pillar of the 'Bull of Iunu' has a pole with a bulbous end that extended the height of a tall stone pillar.  The pillar at Iunu with its pole and bull is similar to the pole with a tethered bull (msxtjw) attached to the top, depicted on the New Kingdom ceiling of chamber C inside TT352, a tomb of Senenmut.

ceiling from the tomb of Senenmut compared to the Pillar of the 'Bull of Iunu'

Mesekhtiu (msxtjw) was the ancient Egyptian name for the large, distinctive 7-star asterism in Ursa Major, known today as the 'Plough' / 'Big Dipper' - it is first attested in the Pyramid Texts of Unis: 

"The sky has been bled and Sopdet lives, for Unis is the living one, Sopdet's son, for whom the Dual Ennead have cleaned the imperishable Striker (msxtiw)."  W 207 (TPMN) (PT 302) Sethe Vol 1: 235  §458c

The top of the pole may represent the North Celestial Pole (NCP), the pivotal point in the sky around which all celestial objects circle.  Mesekhtiu appears to be tethered to this point, endlessly circling around this invisible point in the sky.  Khem is due north from Khufu's pyramid aligned with Thuban the Pole or North Star that closely marked the NCP in the early Old Kingdom.

c. 2781 BC, Thuban was closest to the NCP, the only stationary point of light in their sky around which all other stars revolved.  This era was particularly significant, because the summer solstice and the heliacal rising of Sirius (HRS) coincided within a few days of each other.  The summer solstice roughly coincided with the expected annual flooding of the Nile that was first noticed in southern Egypt.  The exact timing of the inundation varied, as it depended on when the monsoon rains fell on the Abyssinian plateau.  Over the years, Thuban slowly drifted away from the NCP - by the early Old Kingdom it was about one deg or two full moons away distance.  The ancient Egyptians may have noticed this drifting away from the pivotal point in the sky, and attempted to control the situation by establishing a fixed 'pole' at their sacred centre at Iunu.

This Pepi has come to you, lord of the sky.  This Pepi has come to you, Osiris.  This Pepi will wipe your face and clothe you with a god's clothing, having become clean for you in Djedit (Ddt, necropolis of Iunu).  Sothis (spdt), your daughter whom you have desired, [who makes] your [fresh vegetables (rnpwt) in] her identity of the year (rnpt), is the one who led this Pepi when this Pepi came to you.  P 327  (PT 477  §964-5 P;  Sethe Vol 2: 39)   ('year' = D21 (r) N35 (n) Q3 (p) X1 (t) + ideo. M4 (rnpt))

(note:  a possible play on words between 'fresh vegetables' (rnpwt.k) and 'year' (rnpt))

MK reference linking spdt to the year and the beginning of the year:

Sah (Orion) speaks:  'He is my son, older than I (sic)' - so says Sah (Orion)  '....N, who is pure and young, and Sopdet (Sirius) bore him, (even) she the young (rnpii), she of the year (rnpt), a goddess from her birth who is at the start of the year... CT 689  §319 Vol 2: 253

(note:  a possible play on words between 'young' (rnpii), and 'year' (rnpt))

Sirius may have been associated with the inundation as far back as the first dynasty.  An ivory plate from the reign of king Djer shows a cow with a feather (H6) between the horns, and above the 'feather', a dark disk.  Below the cow are three plants on a horizontal base similar to M8, ideogram for the Akhet season (Axt. 'inundation (season)').

prt spdt, 'the coming forth of Spdt' - heliacal rising of Sirius on new year's day.

At least seven Dynasty 4 pyramids were aligned with either Iunu, Khem or Inheb Hedi and the rising or setting of the third brightest star in their sky - Alpha Centauri.  These alignments existed in the early Old Kingdom, but were they intentional?  Does the evidence presented here support these alignments to the extent that its beyond "mere coincidence"?

Without a building instruction manual or the design criteria / specifications of the royal mortuary complexes, no proof is possible, and as these have not survived in the archeological record we can only rely on clues obtained from examining the positional relationships between the royal mortuary complexes themselves and other significant sacred places, and clues from the royal afterlife texts to assess if these alignments were more or less likely to have been intentional.

Apart from obvious practical concerns - topography, good quality foundational bedrock, proximity of quarries etc. that needed to be addressed when planning the royal funerary complex, ideological concerns were also considered - links with important shrines / sanctuaries and other royal funerary complexes.  It also seems likely the bright star, Alpha Centauri, was used as a sighting aid when establishing these links.  In the early Old Kingdom, the mutual alignment of the royal complexes, and their spatial relationship to other important sacred places, appear to have been included at the planning stage, perhaps emphasizing the important role of successorship.  Successive alignments between individual pyramids, temples and sacred shrines can shed light on Old Kingdom ideology, especially when examined in the context of the royal mortuary beliefs recorded within the pyramids themselves from the end of Dynasty 5.

The idea of aligning the royal tomb with a sacred place may have originated as far back as the Early Dynastic Period:  "Certain other aspects of the royal tombs at Abydos hint at the afterlife beliefs of First Dynasty Egyptians.  As we have seen, there is a gap in the line of subsidiary burials surrounding some of the royal tombs;  in each case, the gap occurs at the south-west corner, aligned with the prominant cleft in the cliffs behind Abydos.  Evidence from later periods suggests that the cleft was believed to be an entrance to the underworld;  if this belief was current in Early Dynastic times, the gap in the line of subsidiary burials may have been provided to allow the ka of the deceased king to travel freely from the tomb to the underworld."  (T. Wilkinson 2001 (1999): 256)

chris tedder July 2007

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