Illustration of the ancient Egyptian measure of Seked compared with the slope of the Great Pyramid
Seked (or seqed) is an ancient Egyptian term describing the inclination of the triangular faces of a right pyramid.[1] The system was based on the Egyptians' length measure known as the royal cubit. It was subdivided into seven palms, each of which was sub-divided into four digits.
The inclination of measured slopes was therefore expressed as the number of horizontal palms and digits relative to each royal cubit rise.
The seked is proportional to the reciprocal of our modern measure of slope or gradient, and to the cotangent of the angle of elevation.[2] Specifically, if s is the seked, m the slope (rise over run), and the angle of elevation from horizontal, then:
The most famous example of a seked slope is of the Great Pyramid of Giza in Egypt built around 2550 BC. Based on modern surveys, the faces of this monument had a seked of 5½, or 5 palms and 2 digits, in modern terms equivalent to a slope of 1.27, a gradient of 127%, and an elevation of 51.84° from the horizontal (in our 360° system).
^Gillings: Mathematics in the Time of the Pharaohs 1982: pp 212
^Gillings: Mathematics in the Time of the Pharaohs 1982: pp 212
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