AT SIXES AND SEVENS WITH DASHUR !

In the post “The Pyramids and the Two Skies” a few weeks ago, I had proposed that the Bent and the Red pyramids, as a pair, spatially mimicked the circumpolar stars Mizar and Kocab.

I have now looked for some corroboration for this proposal and one analysis led to something very interesting !

About two years ago Jim Alison pointed out a fact about the line that joined Sneferu’s Pyramid at Meidum to Djoser’s Step pyramid at Saqqara. It bisected the line between the apexes of the Bent and the Red pyramids. In the “Two Skies” theory I claimed that these two pyramids were built deep into the desert, with all the hardship this entailed, just to achieve this bisection.

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(The first picture shows the line from the Meidum pyramid to the Step Pyramid and the intersection of the Bent - Red apex axis. The second pyramid is an enlargement of this intersection. Pictures from Jim Alison)

He then stated that the distance from the Meidum pyramid to the Dashur intersection point was in the ratio of 6 to 7 of the distance from Meidum to the Step Pyramid. This was of interest because the base lengths of the two pyramids were 360 to 420 cubits which was also a ratio of 6 to 7. (see footnote about 360)

This observation was still in the realms of co-incidence until I measured the exact position of the intersection on the Bent-Red axis. It was not mid-way but split the axis again in the ratio 6 to 7 with the 6 on the Red side and the 7 on the Bent side. Now it had become significant !

Petrie gave the distance between the apex of the Red and the Apex of the Bent as exactly 3900 cubits. This is clearly a multiple of 13 (it is 13 x 300) so the intersection point nicely split the line between the apexes into 1800 and 2100 cubits, these being 5 times the side lengths of the two pyramids which are 360 and 420.

(Another way of describing the above information is that the 3900 cubits line joining the apexes was 10 times the average base length which was 390 cubits.)

The axis joining the apexes of the Red and the Bent pyramids was inclined to North at -8.79 degrees (from Petrie). This was the same as the average angle made by 1 on 6 which was 9.46 deg and the angle made by 1 on 7 which was 8.13 deg. So (9.46 + 8.79) / 2 = 8.79 deg.

The Bent pyramid had an outer enclosure that was 100 cubits away from the pyramid making its side length 360 + 100 + 100 = 560 cubits.

It was found by Stadelmann that the Red pyramid once also had an enclosure that was 30 cubits away from the pyramid. Here is his scale drawing from “Pyramiden und Nekropole des Snofru in Dahschur P265 1993”. The pyramid is shown with an evenly spaced enclosure wall broken only near the temple. Using the scale the enclosure is calculated to be 30 cubits from the pyramid. Also we have from the text “auf der N-seite und also vermutlich damit auch auf der Sudseite ca 15-16m = 30 Ellen.” Ellen means cubits.

So the enclosure side length was 420 + 30 + 30 = 480 cubits.

The ratio of the enclosures was thus 560 to 480 - which was 7 to 6. So while the pyramids were in the ratio 6 to 7, the enclosures were in the ratio 7 to 6 ! It is as if they were invertible, as if rotating around a point on the axis.

Note too that the widths of the enclosures were thus 100 and 30 = 130 cubits. This is the sum of 6 and 7 times 10.

So to sum up we have :

1. The ratio of pyramid bases was 6 to 7
2. The ratio of Meidum-Dashur to Meidum-Step was 6 to 7
3. The split in the Bent-Red axis was 6 to 7
4. The distance from the Bent to Red apexes was 3900 cubits (=13 x 300)
5. The angle of the Bent-Red axis was the average of 1 on 6 and 1 on 7
6. The enclosures were in the ratio 7 to 6
7. The pyramid and enclosures sizes were reversible from 6:7 to 7:6
8. The enclosure widths added together were 6 plus 7 times 10.

It is clear that this ratio 6 to 7 was deliberately repeated as a theme and that the spatial positions and sizes of the Bent and the Red pyramids and their enclosures were chosen precisely to incorporate this ratio in several ways.

The question which needs an answer is “what was the importance of the 6 to 7 ratio in the purpose of the pyramids ? Why should the ratio be invertible ?

I did manage to find the answer here : The Kocab-Mizar line in the northern sky in the year BC2540 was split by the north celestial pole (NCP), the point around which all the stars and this line rotate, in the ratio of 6 to 7; 6 on the Kocab side and 7 on the Mizar side.

This means that the point of intersection of the axis joining the Bent and the Red pyramids and the line joining the Meidum-Step pyramids corresponded with the NCP in the northern sky. The figures in the diagram are ratios :



Below is the table of these ratio values between Mizar and Kocab over twenty year periods between 2600BC and 2500BC, (from Dashur using the same inclination) :



As can be seen the ratio of the pole split became exactly 6 to 7 in the year 2540BC. This gives an independent date to the planning of the Bent and Red pyramids. It agrees closely with Dr Kate Spence’s dates.

CONCLUSION

The proposal that the two pyramids, the Bent and the Red, spatially mimicked the circumpolar stars Mizar and Kocab is strongly re-enforced.

(There have of course been many other explanations and symbolisms for the two pyramids. It behoves their proposers to explain the 6 and 7 theme within the purpose of the pyramids.)

Footnote :
The distance between the corner sockets, or where they would have been, was measured by Petrie as an average of 361.6 cubits , (while Dorner claimed it was 362). There was a pavement around the pyramid of which traces remain. Petrie measure it as .63 cubits at one corner above the socket and 1.65 cubits above the socket at another. The pyramid had obviously settled unevenly before the pavement was added. Taking the average pavement height above the socket of 1.14 cubits and with an angle of 54 degrees for the pyramid we get a horizontal distance covered by the pavement of 0.8 cubits. So the pyramid base is 361.6 – 0.8 – 0.8 = 360.0



DJEDEFRE’S ANGLE

Djedefre chose to build his pyramid 8 km northwest of his father’s Great Pyramid at Giza. His pyramid seems to have been intentionally related to the Great Pyramid in several ways. First the height was chosen to be greater by 25 feet because of the higher ground.. This was a part of the desire that we have seen for each king to be one better than the previous king. (See stunning graphics)

Second it was built at 45 degrees north-west from it. The reason for this was presumably geographic, ie that was the location of the high point needed. But the direction was rounded into a perfect half right angle.

It is evidenced that Djedefre completed his father’s complex at Giza, and this included boat pits and also probably the enclosure and the small satellite pyramid. The satellite pyramid was placed just like his own at the south-east corner of the main pyramid thus re-enforcing the 45 degree theme. Up to that time the satellite pyramids had been built due south.

The outer enclosure perimeter of Djedefre appears to have the same perimeter length as that of the Great Pyramid. Within the enclosure there was a unique 45 degree causeway from the enclosure entrance to the east mortuary temple.

So there were links between the pyramids, Djedefre’s and Khufu’s, and a theme of the 45 degree angles.

Assuming the earlier pyramids, the Great, the Red, the Bent and Meidum, were all aligned to the stars Kocab-Mizar when vertical, it gave them an alignment very close to the NCP. Djedefre also aligned his pyramid using these two stars but with a small variation. Instead of the Kocab-Mizar line being vertical, he had it diagonally at -45 degrees and to get his alignment he used Thuban, the pole star alongside the NCP.

The orientation of Djedefre’s pyramid has been measured to be about +48 minutes to true north. By this method (ie. the orientation of Thuban while the K-M line was at -45 degrees) the date this occurred in the sky was around BC2460. Again this independent date is close to Dr Spence’s date.



When he named his pyramid “Djedefre is a sehed star” the star referred to was thus Mizar. While the other Kings of the dynasty oriented the pyramids to the NCP, Djedefre chose instead for his pyramid to be orientated to Thuban which was the star close by the NCP.

Similar to Dashur, the proportional split of the K-M line was incorporated into the base length of the pyramid. The split of the Kocab-Mizar line created by the NCP when the axis was at 45 degrees was once again 6 to 7, see table :



With Khufu’s pyramid base at 440 cubits, the split into ratio 6 to7 is 203 to 237 cubits. The first one, 203 cubits, was the base length of Djedefre’s pyramid and the second one 237 cubits was possibly the average length of the surrounding inner enclosure built around the pyramid.



DJEDEFRE’S AND MENKAURE’S PYRAMIDS

There is a striking similarity between the arrangement of Djedefre’s pyramid and that of Menkaure’s (G3) with the Great Pyramid.

• Djedefre’s lies at -45 degrees to the Great Pyramid (north west), while G3 lies at +45 degrees to the Great Pyramid (south west).
• The base lengths of the two pyramid are the almost same - within 1.5 cubits, 203 and 201.5
• The heights of the pyramids are almost the same about 128 and 124 cubits
• Both pyramids were faced with granite for the lower layers and white limestone above.
• In both cases the 45 degree lines went from the mid-point of their pyramids to the mid point of the Great Pyramid.


Djedefre’s -45 degree line started at the south mid point of his pyramid to the north mid point of Khufu’s pyramid. It also passed through the corresponding west and east mid points of the pyramids

(please check this on Google Earth using the ruler facility, which shows the angle calculated from grid references. To find the centre of the east face of G1, the groove up its west face can be used. The grid references are :

29deg 58 min 44.78secN & 31deg 08min 07.05secE
30deg 01min 55.75secN & 31deg 04min 27.28secE

The reading shown on the ruler panel is actually 135.08 degrees which is 45 degrees south east and 5 minutes. If this accuracy is possible the +5 minutes offset will date the line to 2460BC by Dr Spence’s method.).

Similarly, G3’s 2000 cubit 45 degree line started at the mid south point of Khufu’s pyramid and ran to the north mid-point of G3. See diagram :



So we have an amazing corroboration that the 2000 cubit 45 degree axis at Giza existed and was intentional !

If “Djedefre is a Sehed Star” was the name for his pyramid, then G3 must also represent the SAME star. And that star was Mizar.

Mizar is in fact a double star together with the much less bright Alcor, which can be seen by people with good eyesight. The two stone design - granite around the base and the white limestone above may be symbolic of the double star. The other pyramid representing Mizar was the Bent Pyramid which also can be viewed as two pyramids in one.

So at Giza we have G3 representing the star Mizar with G1 representing Kocab. In between we have G2 representing Thuban.

Khafre’s magnificent plan for Giza and its symbolism will be analysed in the next post, including the reason why G3 was built close to G1 unlike Djedefre’s location.

Graham Chase