I came across this today, and haven't looked at it in any depth, what interested me is that he was identifying various sekeds used in pyramid design involving 1/9th units of fingers, ie a Royal Cubit broken down into 252 1/9ths (28x9=252), an aspect of the Royal cubit they delineated on rulers.



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Regarding the Khafre Pyramid:

With the Royal Cubit consisting of 7 palms of 4 fingers each, the full cubit contains 28 fingers. With each finger then further subdivided into 9ths, there are then 252 of these 9ths to a cubit. The seked of a 27°16' angle therefore can be found to have a horizontal run of 489 of these 1/9th units for each rise of 1 royal cubit (= 252 of the 1/9th units), and so equals 1 royal cubit, 6 palms, 2 1/3rd fingers (which is the same as 1 royal cubit, 6 and 7/12th palms).

The angle of 26°46' can be closely approximated from a finding of 252/500 and so its seked will equal 1 royal cubit, 1 palm and 8/9th palms.

The angle of 21°40' can be closely approximated from a finding of 252/634 and so its seked will equal 2 royal cubits, 3palms, and 2 + 1/2 fingers.




28. The Egyptians referred to angular measure in terms of 'sekeds', with a seked being the number of cubits and/or 'palms' and 'fingers' of horizontal run required by an angle for each vertical rise of one royal cubit. The 27°16' angle, with the stated horizontal run of 489 of the 1/9th units for each rise of 1 royal cubit (= 252 of the 1/9th units), therefore has a seked of 1 royal cubit, 6 palms, 2 1/3rd fingers (which is the same as 1 royal cubit, 6 and 7/12th palms). In a similar manner, the seked for the design angle of the Red Pyramid, with its height to half-base ratio of 17/18, has a seked of 1 royal cubit and 5/12th palms. The design of the royal cubit rod permits its user to choose in each instance a 'finger' subdivision which best suits ease of measurement and numerical manipulation. Interestingly, when each finger is divided into 9 sub-units, thereby giving the royal cubit a total of 252 of these sub-divisions, we find that 8/9ths of 252 is exactly 224, and 11/14ths of 252 is exactly 198. It is possible that this is the subdivision that was the one most often used by the architects both when setting out the initial diagram, and in the subsequent determination of the various seked relationships. See the Computation section for a further discussion regarding the use of sekeds.




Morph.