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Sekeds and the Geometry of the
Egyptian Pyramids
article by David Furlong

A comparison between the angles generated by sekeds and the angles of gradient of the pyramids

Part 1

 picture of The Great Pyramid of Egypt
This article looks at the relationship of the seked to the design of the pyramids of Ancient Egypt with particular reference to the pyramids of the IIIrd to VIth dynasties. It argues that whilst the seked can be clearly perceived in some pyramids it would appear that in others a different, or modified, system was used to calculate their angles of slope.

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'."

In the RMP sekeds are stated in terms of palms and fingers. For example:

"The height of a pyramid is 8 cubits and the base 12 cubits. What is the seked? [5 palms and 1 digit]." RMP 592

diagram of Seked angle

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