Jon: "I'm still not particularly convinced by the 45° diagonal as it doesn't seem to me to join two very obvious points."



Its actually a dual diagonal - the first diagonal connects the centre of the west side of G3 and the centre of the east side of G1 - these are significant points because they lie on the central E / W axis of the pyramid where it intersects with the perimeter of the base.


The second diagonal connects the centre of G3 with the entrance to Khufu's cult complex, and passes through the central niche in Khafra's cult centre.


The entrance to Khufu's cult complex is significant as it lies at the end of the causeway leading to / from Khufu's funerary complex named 'Khufu's Akhet'. In later texts it seems the whole Giza necropolis was known as 'Akhet'. The temple enclosure at Iunu was 45 degs NE, the 'Horus of Khem' shrine at Khem, due north, Djedefra's pyramid, 45 degs NW, and Menkaura's pyramid, 45 degs SW, from this focal point at the entrance to the 'Akhet'. (the pyramids of Djedefra and Menkaura's have a lot in common - they are about the same size, granite was used for much of the casing in both pyramids, and they are both linked to Khufu's funerary complex with 45 deg diagonals)





Jon: "Is a nice "rounded" 2000 cubits really that diagnostic of intent?"




In a OK context yes - it strongly suggests intent. The numbers 20 / 200 / 2000 are found in the context of OK architecture. Khufu's sarcophagus chamber, 20 x 10 cubits; Metjen's Dyn 3 / 4 walled 'estate', 200 x 200 cubits; Mastaba 17 at Maidum, 200 x 100 cubits; the dual Giza diagonal, 2000 cubits.


OK evidence shows that measurements specified in 'architectural' texts were given in whole numbers:

- 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 Dyn 4 tomb of Debehen was designed with specified measurements of 100 x 50 cubits.

- a text from the Dyn 5 Sun Temple of Niuserra mentions a stone structure with a length of 7000 cubits.

- a Dyn 5 text gives the ground plan for Izezi's Dyn 5 Sed festival enclosure as 1000 x 440 cubits.


The 45 degree angle (sqd 7) is also significant as its the diagonal of a square, and was used often in their sacred architecture:


The 45 deg angle 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).


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’), 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.


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. The 'Unfinished pyramid' at Zawyet el-Aryan was named ‘Nebka is a star’ (Edwards).


Alignments with Alpha Centauri, the third brightest star in their sky after Sirius and Canopus 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, Alpha Centauri rose 45 degs south of east, and set 45 degs south of west - a useful bright point of light / star to sight to if an alignment with Iunu was intended.


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)





Jon: "There's another rather nice round number if you join the centre of the North Side of G1 with the centre of the South Side of G3. It's between 2049.793 and 2051.127 cubits depending on which value you use so 2050 would seem to be a reasonable claim particularly with the uncertainty about the base of G3. The angle of this diagonal is 32.345° (on a small diagram it also appears to touch the North East corner of G2 but it actually just misses)."





It misses the NE corner by about 1.5 m. The 32.345 deg E of N angle is very close to sqd 11 (32.471 degs) which may be significant, as a base side of Khufu's pyramid was 440 cubits long, and sqd 11 palms has 44 fingers. sqd 11 can also be expressed as a ratio, 7:11, and this ratio defines the basic form of Khufu's pyramid - the design of the upper north shaft was based on sqd 11.


I extended your line (the blue line) further to the NE just to see how it fitted in with significant alignments between sacred places in the Ineb-hedj / Iunu area. see link: [okadct.googlepages.com] - scroll down to bottom of page.



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)


CT





Edited 2 time(s). Last edit at 09/18/2008 05:43PM by Chris Tedder.