Rules · Proportion · Geometry · Modules
The Great Pyramid of Khufu was laid out 440 royal cubits square and 280 cubits high, a seked of exactly 5½ palms and a slope of about 51°50′.
½ × 440 ÷ 280 × 7 = 5½ palms → arctan(7 ⁄ 5.5) ≈ 51.84°
Modern surveys give a mean base side of about 230.3 m and an original height of about 146.6 m. In cubits of 52.4 cm these are 440 and 280, and 5½ palms is a simple seked for a builder to set out. The four sides differ in length by only a few centimetres and are aligned to the cardinal points within a small fraction of a degree.
Because 440 ÷ 280 is very nearly π ÷ 2, the perimeter of the base is almost exactly 2π times the height; the famous “π relationship” is a consequence of the choice of seked, not evidence of secret knowledge. The next pyramid at Giza, Khafre’s, uses the 5-palm-1-finger seked of the Rhind problems (about 53°).
Specify the slope of a pyramid face by its seked: the number of palms (and fingers) by which the face runs inward for every cubit of rise. The height follows from half the base divided by the seked, times seven.
seked = 7 × (½ base ⁄ height) palms · angle = arctan(7 ⁄ seked)
Lay out Egyptian buildings in royal cubits (≈ 52.4 cm) of seven palms of four fingers, so that every dimension and every slope can be stated in whole or simple fractional units.
1 royal cubit = 7 palms = 28 fingers ≈ 0.524 m
When a steep pyramid shows signs of distress, flatten the slope of the upper part: Sneferu’s pyramid at Dahshur rises at about 54° for its lower part and about 43° above.
lower seked 5 palms (≈ 54.5°) → upper ≈ 7½ palms (≈ 43°)
Cut a shaft with sixteen shallow flutes or facets, give it a square abacus and a low round base: the “proto-Doric” column of the Middle Kingdom rock tombs at Beni Hasan.
Cut the obelisk from a single block of granite, square in section, tapering to about two-thirds of its base width, capped by a pyramidion, and about ten times as tall as it is wide; set them in pairs before the pylon.
height ≈ 9–11 × base width
Find a granary’s capacity from its measures: multiply length, breadth and height in cubits (or, for a round bin, the square of eight-ninths of the diameter by the height), and add half as much again to turn cubic cubits into the grain measure, the khar.
1 cubic cubit = 1½ khar
Cite this page Chris Paton, “The Great Pyramid: 440 cubits by 280”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/seked-khufu. Text, drawings and models licensed under CC BY-NC 4.0.