Sekeds and the Pyramids of Egypt

The Egyptian word 'seked' is related to our modern word 'gradient'."

Sekeds in the design of pyramids

Information on the use of the seked in the design of pyramids has been obtained from two mathematical papyri; the Rhind Mathematical papyrus in the British Museum and the Moscow Mathematical papyrus in the Museum of Fine Arts. The Rhind Mathematical Papyrus (hereafter referred to as RMP) was copied by the scribe Ahmose c.1650BC and is based on a document two hundred years earlier1. Problems 56 to 60 in the RMP deal specifically with calculating the seked of different pyramids, or the height of a pyramid when the seked is known.

The seked is based on the Ancient Egyptian measures of the Royal Cubit, the palm or hand and the digit. The relationship of these measures is as follows:

1 cubit = 7 palms
1 palm = 4 digits

The seked is described by Richard Gillings in his book 'Mathematics in the Time of the Pharaohs' as follows:

"The seked of a right pyramid is the inclination of any one of the four triangular faces to the horizontal plane of its base, and is measured as so many horizontal units per one vertical unit rise. It is thus a measure equivalent to our modern cotangent of the angle of slope. In general, the seked of a pyramid is a kind of fraction, given as so many palms horizontally for each cubit of vertically, where 7 palm equal one cubit. The Egyptian word 'seked' is thus related to our modern word 'gradient'."

Sekeds and the Pyramids of Egypt


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