Don,

518 x 183 m; 515 x 180 m; 500 x 185 m – perhaps these measurements are a mix of inside and outside measurements of the enclosure (the walls are over 3 m thick), which might explain some of the differences.


The enclosure is made up of three areas: a central rectangular area where the longer side is more or less the length of the diagonal of a square with sides equal to the shorter side, a square extension to the north, and a 1 : 2 rectangular extension to the south. The width of the enclosure is about a third of the overall length.


I don’t have the original survey measurements, only a plan of the enclosure in Lauer’s book ‘Saqqara’ (Lauer 1976: 139), where the measurements are in cubits.

According to Lauer’s drawing, the step pyramid is in the centre of a 500 x 348 cubit enclosure. To the north is a 354 x 348 cubit extension, and to the south a 174 x 348 cubit extension.

Overall inside length / width of the enclosure: 1040 x 348 cubits.

Overall outside length / width: 1052 x 360 cubits (enclosure walls: 6 cubits thick (~3.142 m).


It would be interesting to see the original survey measurements, as there is a tendency with long distances to round up or down to the nearest whole cubit or even to the nearest ten cubits when converting metres to cubits.


Lauer’s width measurement is different from that given in the Giza Mastaba’s series (No. 7, p. 98):

“If the dimensions of the S given in Inti’s inscription are indeed 1,000 x 440 cubits, that is, 525 x 231 meters (see further note f), it is perhaps worth mentioning that these dimensions are roughly the same as those of the pyramid complexes of Djoser and Sekhemkhet at Saqqara (544 x 277 m and 536 x 272 m respectively; see Swelim, Third Dynasty, p. 33).”


The “272 m” width is probably a ‘scribal’ error. According to Lauer, Netjerikhet’s enclosure is 544.8 x 276.85 m (~1040 x ~529 cubits), so perhaps the width of Netjerikhet’s and Sekhemkhet’s enclosures are getting mixed up here.


The stone courses in Sekhemkhet’s enclosure walls are 50 – 52 cm (~1 cubit) high, double the height of the 24 – 26 cm high (~1/2 cubit) courses of Netjerikhet’s walls (Lauer 1961: 15; Goneim 1957: 2).

CT

.... Graham: “I think that not much more analysis is worth doing until the dimensions differences are resolved;

Barone (Goneim) 518 x 183 metres
Tedder (Lauer) 1052 x 360 cubits (551 x 189m)

and whether these are inside or outside measurements with a wall thickness of 6 cubits.”



According to Lauer’s drawing, the inside width of the northern extension is 348 cubits and the outside width, 360 cubits – difference =12 cubits, which means the walls are 6 cubits thick.

A more detailed drawing of the central area in ‘The Pyramids of Egypt’, shows the walls of the northern extension stepped in by ~3.5 cubits, which means the east and west walls of the central area are ~9.5 cubits thick. The overall outside width of the central area is then 367 cubits, but the inside width remains the same as the inside width of the extension (348 cubits).

“the excavator stated that the eastern and western walls, in their northern extensions, were not in direct alignment with the earlier walls, each being stepped in by about 6 feet……” (Edwards 1985 (1947): 63; Fig. 14)


According to Lauer, 1052 x 360 cubits are the overall outside dimensions (~551m x ~189m).

The overall inside dimensions are: 1040 x 348 cubits (~545 x ~182 m), so the largest discrepancy with “Barone (Goneim) 518 x 183 metres” (which appear to be inside dimensions), is in the length: 518m or 545 m. ...

Tedder (Lauer) 1052 x 360 cubits (551 x 189m)

On another board, namely Graham's, Jonny did for me an exhaustive search and study of the data in The Saqqara Ostracon and here is what he had to say:

... So in summary, if you were wanting any hard analysis done, then it was being done with an ellipse. Also, I would conclude that the shape lies on an ellipse of semi-major axis 255.8612 and semi-minor axis of 178.0540 with 99.98% agreement between fit and data, regardless of what other people say. What's more, if that coordinate was meant to be 85 instead of 84 as Dr Trog points out, then the ellipse is one of 256.1136 x 177.9399 with a 99.998 % agreement between fit and data. This makes me think that if we are dealing in whole numbers of units that it is a 256/178 ellipse, which is a/b = 1.4382.

Now I did everything in my power to sway his decision but he was adamant that given the 6 points in question this was the size for a best fit ellipse. He was unwavering in his belief that he had calculated it correctly. Even lobo and Warwick joined in to poke fun at my apparent lack of understanding.

However perhaps I may have the last chuckle in this instance for we have these two "facts" presented to us now.

the step pyramid is in the centre of a 500 x 348 cubit enclosure.

and the best fit for The Saqqara Ostracon as

semi-major axis 255.8612 and semi-minor axis of 178.0540

Step Pyramid enclosure = 500 / 348 = 1.43678161

semi-major axis 255.8612 / semi-minor axis of 178.0540 = 1.43698653

Degree of accuracy this time is:

1.43698653 -
1.43678161
===========
0.00020492

or

99.986

It would now appear that the first part of the construction was drawn to the scale of The Saqqara Ostracon and in fact it also now appears that rather than just the arches here it actually designed the lay out of the first enclosure as well.

Over to you Warwick and lobo and Anthony



Don Barone

PS: Yes it is true. He who laughs last laughs best.



"There is nothing as impenetrable as a closed mind"
and ..." if everything is a coincidence what is the point of studying or measuring or analyzing anything ?" db