djedefragiza

Djedefre (or Radjedef) / Giza

Khufu's successor, Djedefre, built his mortuary complex 8.3 km NW of Khufu's mortuary complex, on a high plateau overlooking the river Nile.  The mortuary complex of Menkaure (Khufu's grandson) is SW of Khufu's funerary complex.

Two, 2000 cubit (20 khet) long, 45 deg diagonals, linking Menkaure's pyramid with the funerary complex of Khufu, aligned the Giza pyramid group with the temple enclosures with their pillars and shrines, and Djedeu / Djedit the 'mound' / necropolis of Iunu, 45 degs and 440 khet to the NE.  Djedefre's pyramid, 45 degs to the NW, mirrors this alignment.

(side length of Khufu's pyramid = 440 cubits.  440 x 100 = 440,000 cubits = 440 khet)

Four inscriptions 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 designed with specified measurements of 100 x 50 cubits.  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 Dyn 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), and ~20 cubits high.  Sekhemkhet's enclosure to the southwest is similar in size, and another enclosure further to the south west is even larger.

Horus, the god of kingship is 1000 cubits long:

"To be Hetep (Htp), Lord of the Field of Offerings.  This is Horus of the Tree(?), he is a falcon, he is a 1000 cubits long, life and equipment are in his hand, he comes and goes at will in its waterways and towns, he rises in the birth-place of the god and he sets in qnqnt, he does everything in it as is done in the Island of Fire, there will be no shouting at all in it and there will be nothing evil in it."  CT 465 V, 349

The names of the pyramids of father and son highlight the 45 deg SE alignment with a shining star rising above the 'horizon' of Khufu.

To an observer standing on the south side of Djedefre's funerary complex, Alpha Centauri, the third brightest star in their sky, rose above the SE horizon from behind Djedefra's father's funerary complex at Giza, 45 degs SE.  The name of Khufu's pyramid was 'Khufu's Akhet' ('Akhet' associates his pyramid with becoming an Akh and rising from the horizon - according to the PTs, akhs were the northern Imperishable Stars), and according to N.C. Strudwick, the name of Djedefre's pyramid was 'Djedefre is a shining star'. (Strudwick 2005: xxix).

The 45 deg diagonal extended SW from Menkaure's pyramid, marked an area on the horizon where the triple star system of Alpha Centauri set during the era when these pyramids were built.

One of the two diagonals connects the centre of the west side of G3 with the centre of the east side of G1, and the other parallel diagonal connects the centre of G3 with the entrance to Khufu's cult complex on the east side of his pyramid.

The entrance to Khufu's cult complex lies on the east - west axis of his pyramid about 53 m from the centre of the east side of the pyramid:

"In a north-south sense the temple was 52.40 m long, i.e. 100 cubits.  Its facade was 53.35 m (about 102 cubits) from the pyramid base and about 40.30 m (77 cubits from the temenos wall exterior face.  We have taken these measurements from one of Lauer's plans.  The outer faces of the temple walls were made of limestone and the north, east, and south walls were about six cubits wide at the base (about 3.14 m)."  (M&R Part 4,1967: 60)

These two parallel 2000 cubit long, 45 deg diagonals may reflect an aspect of the dualism that pervades ancient Egyptian symbolism.

According to Petrie's survey, the 2000 cubit, 45 deg diagonals are ~1047.6 m.

1047.6 m / 2000 = 0.5238 m, which is to all intents and purposes, identical to the estimated original length of the cubit used in the royal mortuary complexes at Giza:

"On the whole we may take 20.62 ± .0I (0.52375 m) as the original value, and reckon that it slightly increased on an average by repeated copyings in course of time." (Petrie 1883: 181)

note:  cubits rods from a later period, are ~524 mm long

The 2000 cubit long, 45 deg parallel diagonals:

G1 (centre east side) to G3 (centre west side):  45 degs SW;  distance, 2000 cubits (blue line)

G1  (entrance to cult complex (upper temple) at the top end of the causeway) to G3 (centre):  45 degs SW;  distance, 2000 cubits (brown line):

G1 (entrance to cult complex at the top end of the causeway), to the pyramid of Khufu's son (or possibly brother), and successor, Djedefre:  45 degs NW  - mirrors G1 (entrance to cult complex) to G3 (centre):

Detail of the alignment hub at the entrance of Khufu's cult complex (upper temple), east side of pyramid: 

The same 45 deg NW bearing from the entrance to Khufu's cult complex to the centre of Djedefre's pyramid, is also found in the 45 deg NW azimuth of the causeway that connects the entrance to the cult complex on the east side of Djedefre's pyramid with the entrance to the enclosure around the pyramid.  The entrance on the north side of the enclosure is located on or very close to the NS centre axis of the pyramid:

A similar symmetrical layout also links the centres of G1 / G3 with Djedefre'spyramid:

The bearing from the centre of Menkaure's pyramid (G3) to the centre of Khufu's pyramid is ~52.2 degs NE.  This mirrors the bearing from the centre of G3 to the centre of Djedefre's pyramid, ~52.2 degs NW, a distance of ~16000 cubits.

G3 (centre) to G1 (centre):  ~52.2 degs NE

G3 (centre) to Djedefra's pyramid (centre):  ~52.2 degs NW - mirrors the NE bearing to G1:

The ~52.2 degs Menkaure / Djedefre sightline, extended to the north western horizon, marked the area where Vega, the second brightest star in the northern sky set. The ~52.2 degs Menkaure (G3) / Khufu (G1) sight line, extended to the north eastern horizon, marked the area where Vega rose.

As Vega set, Thuban, the then North or Pole Star, was a few arc minutes west of due north, a useful point of light to sight to for finding north. The pyramids of Khufu and Khafre are accurately aligned to the cardinal points, the mean deviation from north for both pyramids is ~4' west of due north.

Thuban, closely marked the North Celestial Pole (NCP) to within a few arc minutes c. 2787 BC (Early Dynastic period), and if sighted to on any clear night throughout the year using a backsight and foresight, a north / south direction line could easily have been determined.

By the early Old Kingdom (OK) however, Thuban had gradually ‘drifted’ away from the NCP, but was still close enough to be used as a sighting aid for finding true north. To a casual observer in the early OK, Thuban still appeared as a more or less stationary point of light, but a vertical straight edge set up with a plumb line would have enabled surveyors to determine that Thuban actually circled around an invisible point in the sky (the NCP), once every 24 hours - its highest and lowest point in the sky, marked due north.

Khufu's reign began around 2589 BC, and an hour after the sun had set at the winter solstice, Vega was visible setting over the north western horizon, and at this moment, the 'North / Pole Star, Thuban was a few arc minutes west of due north at its lowest point in the sky below the NCP. If the surveyors had chosen this 'potent' moment to sight to Thuban, then this would explain why the pyramids of Khufu and Khafre are accurately aligned to the cardinal points, but just a few arc minutes west of due north.

Aligning the pyramids of Khufu and Khafre to the cardinal directions, and observing the bright star Vega as it set after the sun had set at its furthest point south along the western horizon, and simultaneously sighting to the the North or Pole Star Thuban

Along with Deneb and Altair, Vega is the brightest of the three stars in the 'Summer Triangle'.

The ~52.2 degs Menkaure (G3) / Djedefre sightline, extended to the north western horizon, also marked the area where Arcturus, the brightest star in the northern hemisphere, set. Viewed from Menkaure's mortuary complex, Arcturus setting over the north western horizon, appeared to 'enter' Djedefre's pyramid.

The ~52.2 degs Menkaure (G3) / Khufu sight line, extended to the north eastern horizon, marked the area where Arcturus rose. 

“Arcturus, or α Bootis, lights northern spring skies with a soft orange light. At magnitude -0.05, it is the brightest star in the northern hemisphere, and the fourth brightest star in the night sky (following only Sirius, Canopus, and Alpha Centauri). Arcturus, whose name means ‘Bear Watcher,’ follows the Great Bear, Ursa Major, around the pole. The Greek word for bear is ‘arktos’, from which our word ‘arctic’ is also derived, in reference to the northern polar constellations of the Greater and Lesser Bears. At 37 light-years away, Arcturus is the closest giant star to Earth. Its light was used to open the 1933 Chicago World's Fair, as that light had left the star during the previous Chicago World's Fair in 1893.”  (source:  SkySafari Pro 1.8)

Chris Tedder - spring 2008 (updated from an earlier 1999 web page)