Geometrical models

Approximation and seked

In order to give a quick and clear impression, the slopes of the pyramids in the list have been expressed in degrees. Some measurements are more precise than others, and can be expressed in degrees, minutes and sometimes also seconds. However, the extreme precision of such data may be misleading, since virtually all the measurements have been taken from small surviving parts of the casing and sometimes even from loose blocks.

Of course every slope, even those differing from one another by a fraction of a degree, can be expressed in an equally detailed way by means of cubits, palms, fingers and smaller fractions. It is worth asking, though, if extreme precision is really important. Was it really possible to control fractions of degrees in the largest pyramids? The final smoothing of the faces removed quite a lot of extra stone, and slight mistakes and imperfections of the surface must have been corrected by this last operation. The precision of the construction is certainly documented, whenever they have survived, by last courses of casing blocks and pyramidia, but, for the whole surface of entire pyramids, a certain approximation should be allowed. It is probably useless to make a distinction, for example, between the 51°40′ of Queen GIc, the 51°50′ of Queen GIa and GIb, the 51°52′ of Meidum and the 51°53′ of Khufu, or between 56° of the satellite of Sahura and Senusret III and 56°18′ of Unas, or between 54°30′ of Amenemhat III at Dahshur and Khendjer and 54°21′ of Queen Atmu-Neferu, and probably even between all the values ranging from 54° and 55°23′ measured by Petrie along the very irregular lower part of the Bent Pyramid.