Hi, I Cooper,
The seked did most certainly govern the gradient of all interior passageways. The real question is what are the possible design sources and reasons for any particular seked to be applied as done in problem #57 of the Rhind Mathematical Papyrus?
You wrote:
I believe that the seked was a tool that could be used to describe a slope that had been predetermined by other desired requisite needs.
You are correct! Just to arbitrarily calculate the seked from x/y dimensions with no source or supporting evidence for the use of that particular seked is pretty much just speculation.
There is always a reason for the use of any particular seked.
You wrote:
For construction purposes, once a height and run had been decided upon, a template was likely made for the masons to use - such as the 25 by 18 right triangle of RMP 56.
Why would a template be necessary? Since you mentioned Rhind Mathematical Papyrus Problem 56.To make a point, please allow me to digress for a moment and examine problem 56.
Cause thou that I know the seked of it. You are to take half of 360; It becomes 180. You are to reckon with 250 to find 180. Result: 1/2 + 1/5 + 1/50.
A cubit being 7 palms, you are to multiply by 7.
1 ---- 7
1/2 --- 3 + 1/2
1/5 --- 1 + 1/3 + 1/15
1/50 --- 1/10 + 1/25
Its seked is 5 1/25 palms.
How does one calculate 1/25 palm? 1/25 palm divisions are not normally found on any cubit rod. The smallest subdivision on any cubit rod is 1/16 digit. How does one determine 1/25 palm or 4/25 digit when it fails to coincide with the subdivision markings found on the cubit rods?
The run rise of the seked is given in the statement:
You are to reckon with 250 to find 180.
This statement assumes the reader knows and understands unit fractions. Would it mean divide the length of the base by height to achieve a fractional value from which unit fractions 1/2 + 1/5 + 1/50 can be extrapolated using any of the methods demonstrated in the 2/n tables.
180 / 250 = 18/25
18/25 minus 1/2 = 11/50 = (1/5 + 1/50)
11/50 minus 1/5 = 1/50 given this is a unit fraction so no further extrapolations are required. Yielding the Result: 1/2 + 1/5 + 1/50 which when added equals the original 18/25
Which brings us back to:
A cubit being 7 palms, you are to multiply by 7
1 ---- 7
1/2 --- 3 + 1/2
1/5 --- 1 + 1/3 + 1/15
1/50 --- 1/10 + 1/25
Its seked is 5 1/25 palms.
Why not just tell the masons 18 palm run to 25 palm rise. I prefer to believe, like you and I, the masons were thinking human beings and the masons building the pyramids were educated in the mathematical ways of their time. Therefore no template would be necessary for effective communication between architect/designer/supervisor/mason, just the run rise ratio of the seked.
All of the above is just my humble opinion.
Regards,
Jacob
