> Hi Lee,
> I just took another look at Ancient Egyptian
> Science: Ancient Egyptian Mathematics, by Clagett.
> In the text he mentions the description by
> Lepsius of the remen length on one of the cubit
> rods, but take a look at his illustrations of
> cubit rods at the back of the book. The first
> illustration, of the wooden cubit rod at Turin
> (Fig IV.24.1) which he references to Lepsius and
> which is the one I think he is talking about in
> the text, shows the royal cubit hieroglyph over
> digits 25-28, shows the short (6 palm) cubit
> hieroglyph over digits 21-24, and shows the remen
> hieroglyph over the fifth palm (digits 17-20).
> Figure IV.24.2 on the next page does not show the
> hieroglyphs for the royal cubit, the standard
> cubit, or the remen. Figure IV.24.3 is a broken
> up stone cubit rod at Florence and reads from
> right to left, and digits 21-24 are missing, but
> you can see the royal cubit hieroglyph over digits
> 25-28, and the remen hieroglyph over the fifth
> palm (digits 17-20). Figures IV.24.4 and IV.24.5
> do not show the hieroglyphs for the royal cubit,
> standard cubit, or remen. Fig IV.24.6, from
> Alexandria?, shows the remen hieroglyph over the
> fifth palm (digits 17-20). Figures IV.24.8 and 9
> do not show the hieroglyphs for royal cubit,
> standard cubit, or remen. Fig IV.24.10 is I think
> a reproduction cubit rod at Leiden of the Fig
> IV.24.6 cubit rod, and it also shows the remen
> hieroglpyh over the fifth palm (digits 17-20).
> According to the article from the Met Museum cited
> in my article (also cited elsewhere) the gold
> plated cubit rod at Turin also shows the remen at
> the fifth palm (digits 17-20), and also the cubit
> rods at Cairo I cited above from de Lubicz. My
> understanding is that the surviving cubit rods
> that have the hierophlyphs for the royal cubit and
> the short cubit, also have the hieroglyph for the remen.
There are indeed several cubit rods that show the remen as 5 palms, but still no textual evidence of the remen in the literature, except for RMP 49, which refers to a "remen ifd" (rectangle) using the Gardiner sign D41 for remen. The rectangle described has dimensions 2 khet x 10 khet, and the student is asked to find the resulting acreage. The workings to this problem show that the remen means half the area, which does not jive with the meaning of half-diagonal of a square. Jose Galan has said the remen of the rectangle refers to the right triangle formed by the diagonal and which cuts the rectangle in half, hence is half the area.
As confusing as this may sound, RMP 49 is the only papyrus that ever uses the remen sign, but it is not in the context of a measure of 5 palms.
On the other hand, I am in the middle of reading Lumpkin's article "The Mathematical Legacy of Ancient Egypt," and she cites an 1892 article by Griffith which refers to an inscription at Edfu using the remen sign to describe half a setat, which is configured as 50c x 100c. The side of the square which generates the half-setat IS the half-diagonal of the setat (100c x 100c square), which is 70 cubits 5 palms (or 495 palms). This produces the √2 values of 99/70 and 140/99.
These are the √2 values found in the pyramid bases. The pyramid of Userkaf, with its base of 140 cubits, has a whole cubit diagonal of 198 cubits, demonstrating the two canonical values of √2.
Here is Griffith's 1892 article. [www.mindserpent.com]