|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
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
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
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
or full article download
or text only article