As I described in my article, “The Slope of the Great Pyramid,” the ancient Egyptians described angles in terms of their cotangents. The royal ell contained seven palms, and a slope of six palms horizontal run to seven palms rise (to us, a 49° 23′ 55″ angle) was to them an angle of six palms.
The table below gives the slope angles for the pyramids as given by Greenwood. Also given are the slopes in palms per ell, and the percentage difference between the cotangent of the angle given in degrees and the cotangent of the probable intended angle in palms per ell.
Except for the upper slope of the “Bent” pyramid, the angles fit remarkably well. (I consider my 7 3/7 and Greenwood’s 17/18ths equally unconvincing.) The fractions 1/4, 1/3, 1/2 and 2/3 were commonly used by the Egyptians. I think the data speak for themselves.
| Pyramid | Slope (degrees) | Slope (palms/ell) | Error |
|---|---|---|---|
| Meydum | 51° 53′ | 5½ | 0.15% |
| “Bent” (lower) | 54° 31′ | 5 | 0.2% |
| “Bent” (upper) | 43° 21′ | 7 3/7? 17/18? | 0.18% or 0.047% |
| Dashur (north) | 43° 40′ | 7 1/3 | 0.004% |
| Cheops | 51° 50′ | 5½ | 0.034% |
| Chephren | 53° 10′ | 5 1/4 | 0.13% |
| Mycerinus | 51° | 5 2/3 | 0.03% |
R. J. Schadewald
March 1977