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Sekeds and the Geometry of the
Egyptian Pyramids
article by David Furlong

A comparison between the angles generated by sekeds
and the angles of gradient of the pyramids

Part 2

 picture of The Great Pyramid of Egypt

Assessing the angle of slope of existing pyramids

The majority of all Egyptian pyramids are now in such a state of ruin that it is very difficult to assess the original height of the pyramid even if the base measurements can be accurately determined. In the few preserved pyramids there are a number of methods that can be used. The first involves measuring the slope of the remaining casing stones. It has been found that slight local variations occur. Averaging these give an approximate guide to the height of the pyramid. An example is the pyramid of Pepi II which I.E.S. Edwards estimated as being 171 feet and a base of 258 feet3. This gives an angle of slope of 52.97ø determined from a few casing stones.

Flinders Petrie in his measurement of the Great Pyramid listed the angles of slope from the remaining casing stones as:

Casing stones in situ on N. face = 51°-46'-45"

Casing stones 5 overturned = 51°- 52'

Casing stone fragments (18 no) = 51°-53'-4"

 

casing stones of the Red Pyramid
Casing stones of the
Northern Stone pyramid of Seneferu

To supplement these calculations Petrie carried out a number of additional checks involving accurately surveying the corner stone inclines and the height to the final existing level. This method has been adopted by other surveyors where applicable. None of the capstones, or pyramidions remain so completely accurate assessment is not possible. Nevertheless a very close approximation can be given particularly with the better preserved pyramids. Using all of these methods Petrie arrived at a figure of 51°-52' +/- 2' for the angle of slope of the Great Pyramid. Other pyramids on the Giza plateau had slightly greater variations depending upon their state of preservation. For example the pyramid of Menkaure is given as 51° +/- 10'.

Based on these methods the angles of slope of the best preserved pyramids from the IIIrd to VIth dynasties can be listed as follows:

Maidum:
N. Stone Pyramid:
Bent pyramid(1):
Bent pyramid(2):
Khufu:
Khafre:
Menkaure (a):
Menkaure (b):
Userkaf:
Sahure:
Neferikare:
Nyuserre:
Teti:
Pepi II:
51.88°
43.6°
54.52°
43.35°
51.87°
53.13°
51.19°
51.85°
53°
50.19°
53°
51.85°
53°
53°
The pyramids of Khaffre and Khufu
The Pyramids of Khafre and Khufu

(Note: Recent evidence suggests that the pyramid of Menkaure was not set on a square base; one side being 335 feet whilst the other 343 feet. This will produce two different angles of slope one of 51.85° and the other of 51.19°.)


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