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

Part 6

The Pyramid of Menkaure

The evidence from Menkaure's pyramid further supports this conclusion. As already stated Petrie gave the angle of slope of Menkaure's pyramid as 51° +/- 10'; whilst the figures from I. E. S. Edwards suggest an angle of 50°- 43'. The nearest equivalent seked to 51ø is 5.75 which equals 50°- 36' or 5.5 which equals 51°- 51'.

Mark Lehner in his book The Complete Pyramids suggests that the base of Menkaure's pyramid is not square measuring 343 feet on one side and 335 feet on the other. If these figures are correct and the Egyptians built to a whole number of cubits then the longer side was probably based on 200 cubits and the shorter on 195 cubits. Applied to the pyramid this would give two angles of slope; one of 51.85° and the other of 51.19°. If these measurements are correct two different sekeds would have to have been used.

If the same idea, for the Northern Stone Pyramid of Sneferu, is applied to the pyramid of Menkaure, using a 5/7 seked ratio, then the angle of slope could be shown to be 4.00 sekeds which gives an angle of slope of 51.34° (51° - 20' - 25"). If this seked is correct then the height to base ratio is 5 to 8 for one of the angles of slope. Unfortunately this ratio does not easily fit to the other angle of slope which has a ratio of 7:11. This becomes apparent when the measures are converted to cubits.

As already states the longer side of 343 feet gives a length of almost exactly 200 cubits. This figure is divisible by 8 (200 / 8 = 25) and would give a theoretical height for the pyramid of 125 cubits. The shorter side would appear to be 195 cubits but in this case the number is not easily divisible by 11 (195 / 11 = 17.727), nor is the height of 125 cubits readily divisible by 7.

We might conclude that either the present measurements have not been determined with sufficient accuracy to draw conclusions or the builders failed to make the sides of this pyramid equal through faulty measurement. Because of the problems generated by two separate sekeds derived from a rectangular base it is very unlikely that an inaccurate ground plan could have gone un-noticed in the early stages of construction and not have been corrected. This suggests that, if the sides were not originally intended to be equal, then two separate sekeds were a deliberate aspect of the design. What these might have been cannot be easily determined.

Summary

Whilst the use of the seked, as indicated in RMP, can be clearly perceived in the design of a number of pyramids it cannot be conclusively shown to have been used in all. It is most likely that variations were used for specific reasons. With very few exceptions the ratios do not fit with basic building practice which would normally prefer to work with primary palm ratios such as 7 to 5. Instead we find the use of part palm ratios in almost all known pyramids. The only conclusion is that the symbolism of the ratio was more important than the ease of building practice. As has been demonstrated sekeds of 5.25 and 5.5 incorporate the 3 : 4 : 5 triangle and a relationship to circle respectively. It is therefore likely that it was these symbolic or cultic aspects that were deemed to be important in the design of the pyramids.

Notes:
1. Reading the Past: Mathematics and Measurement O.A.W. Dilke British Museum Press 1987
2. Mathematics in the Time of the Pharaohs Richard Gillings. Dover (NY) 1972
3. The Pyramids of Egypt I. E. S. Edwards. Ebury Press 1947
4. The Pyramids and Temples of Gizeh William Flinders Petrie. Field and Tuer 1883
5. The Pyramids Complete Mark Lehner. Thames and Hudson 1997
6. Mathematics in the Time of the Pharaohs Richard Gillings. Dover (NY) 1972
7. Mathematics in the Time of the Pharaohs Richard Gillings. Dover (NY) 1972
8. Egyptian Pyramids Leslie Grinsell John Bellows 1947

Other links articles:

Abydos - Temple mysteries

Egypt tour : Eleven day tour in April 2005 and in November 2005

The Keys to the Temple - Mystery patterns in the British landscape showing pyramid geometry.

Site Map - List of all David Furlong's articles.

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