Kanga Wrote:
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> The seked is calculated from the vertical and
> horizontal components of the GG and AP, but these
> are difficult to establish, as Legon has shown.
>
> Based on Petrie's measures, Legon suggested that
> the heights of the GG and AP are 39c and 33c
> respectively, but that their runs are not whole
> cubits. Rather, their sloping lengths are whole
> numbers of cubits, 88c and 75c respectively.
Thinking more about this, this is not quite right. The GG has whole cubit run and rise values, so the seked is fairly easy to calculate for a competent mathematician.
The AP, on the other hand, has a seemingly irrational square root, definitely fractional, horizontal measure, making the seked calculation very difficult. One has to use Pythagoras' Theorem to establish what square root is required. It is sqrt 4536 = 67.3498... cubits.
They needed to know the horizontal measure (run) of the AP, and add it to the GG's run of 79 cubits, so as to control the location of the junction of the DP and AP (marked by the floor joint).
The real difficulty is calculating the square root. They may have used Hero's three-step algorithm to do it.
I have my doubts that they used a set square (Legon's "template") based on a 75c diagonal against a 33c height to control the slope of the AP. To make the template they would still have needed to know the base of the right triangle in a rational form. In any case, the AP's run is close to 67 + 7/20 = 498/20 cubits. It may have been left in this form to make seked calculations easier.
Seked = 498/20 x 7/33 palms
= 9429/660 palms
= 14 + 1/4 + 2/55 palms
= 14 + 1/4 + 1/33 + 1/165 palms to three unit fractions;
or = 14 + 1/4 + 1/28 palms to two unit fractions.
This is all speculative of course.
Whatever seked they used, its purpose would have been to get as close as was practicable to a sloping length of 75 cubits.
Hail Atlantis.