Kanga: "If you are implying that this 45* line is the Heliopolis alignment, you would be wrong. If any line pointed to Heliopolis, it would be the line connecting the SE corners..."
Its a popular myth that all three SE corners are in line.
Lehner's description: "A great SW - NE diagonal cuts the diagonal of Men-kau-re's first queens pyramid, touches the SE corner of his pyramid, cuts the diagonal of his Mortuary Temple, passes the SE corner of the Khafre Pyramid court, cuts the diagonal of the fore-temple of Khafre's Mortuary Temple, touches the SE corner of Khufu's Pyramid, very nearly cuts the diagonal of his first Queen's Pyramid, and ends in a large block of masonry built into the escarpment."
Note, Lehner makes no mention of the line "touching" the SE corner of Khafra's pyramid (G2). His "great SW - NE diagonal" only connects two of the three corners - the SE corners of G3 and G1, and the line completely misses the SE corner of G2 by about 12 m (~40 ft).
Lehner's "great SW - NE diagonal" (G3 / G1 line), has a bearing of ~46.7 degs N of E, an angle worth noting as its integral to the geometry of a sqd 5 1/4 pyramid - G2 is a sqd 5 1/4 pyramid, so perhaps this line between G3 and G1 was significant for other reasons.
A line connecting the SE corners of G1 and G2 extended to G3 will miss the SE corner of G3 by 20....23 m (65....75 ft) - if it was intended that the SE corners should all be aligned, the accuracy over this distance would have been to within a few metres, not tens of metres.
If this "great SW - NE diagonal" (~46.7 degs N of E) that connects the SE corners of G3 and G1 is extended NE towards Iunu, it misses the temple enclosure as they are 'mapped' in Quirke's 'The Cult of Ra' - its too far north, but its still in rough alignment with Iunu, so again, it may well be significant.
My proposal for an alignment with Iunu, specifically 'targets' the temple enclosure - its based on alternative 'Giza diagonals' - the 45 deg, 2000 cubit long diagonal connecting the centre of the west side of G3 with the centre of the east side of G2, extended to the NE, aligned with the temple enclosure at Iunu, as was a parallel 45 deg, 2000 cubit long diagonal from the centre of G3 to the entrance to Khufu's cult complex.
Some reasons why these diagonals are worth noting:
- a 45 deg diagonal is the diagonal of a square, which the AE were very familiar with.
- they are each 2000 cubits long
- are accurately aligned with the temple enclosures at Iunu
- a 45 deg diagonal that mirrors these diagonals connects the entrance of Khufu's cult complex, with Djedefra's pyramid, 45 degs to the NW. Djedefra was of course Khufu's son or brother, so its all very much a family affair.
One of your objections to my proposed 45 deg diagonal is that its "not exactly 45 degrees" - of course its not exact - do you really expect the AE were capable of pinpoint accuracy over a kilometer???
The diagonals of the base of G1 are not "exactly" 45 degs either, so does this mean the base of the pyramid was not intended to be square? (Cole has the NE / SW diagonal, 44,95 degs, and the NW / SE diagonal, 45.05 degs) The AE surveyors set out to achieve a square base, but it would have been virtually impossible, with the simple equipment available to them, to achieve an "exact" 440 x 440 cubit square - reasonable tolerances that are consistent with ancient surveying methods and building construction need to be allowed for here.
The 2000 cubit long 'Giza diagonal' is only about a 1/10th of a deg off 45 degs, so considering the simple 'equipment' they were working with and the distance involved, rather than stating its not "exactly" 45 degs, we should appreciate the accuracy of their surveying methods.
Another of your 'objections' is that the 45 deg line "does not pass through any significant point in Khafre's base" - well neither does the Lehner line you prefer, but you did not mention you object to that. The Lehner line misses the SE corner by about 12 m (~40 ft), less 'accurate' than the 45 deg diagonal that 'misses' the centre of the east side of G2 by about 9 m (~29 ft), but I have never claimed it was intended to align with this point anyway - at this scale, ~9 m is too great an inaccuracy for it to suggest an intended alignment with this particular point.
The basic design of Khafra's pyramid is based on a different (sqd 5 1/4) geometric scheme to the others, with its own unique positional relationship with G3 and G1 - it is however, fully integrated into the overall scheme that appears to have been based on a series of squares and their diagonals, perhaps as an aid in ensuring an ordered development of the Giza plateau with a direct link to the religious centre of Iunu.
CT