RLH Wrote:
-------------------------------------------------------
> MJ Thomas 2 Wrote:
> > For the most part I see the seked 5 1/2 not in
> > terms of a modern ratio - i.e. 14/11 - but as the
> > AEs saw it (according to the Rhind Mathematical
> > Papyrus) i.e. 1 royal cubit rise to 5 1/2 palms
> > horizontal run.
> > I hypothesise that this seked was seen also as 28
> > digits rise to 22 digits horizontal run, and that
> > this led to the Pyramid being made 280rc high and
> > 220rc half a side.
> >
> > MJ
>
>
> Hello MJ
>
> It’s never good to mix apples with oranges. So I
> would not say 1 cubit rise to 5 ½ palms run,
> instead I would say 7 palms rise to 5 ½ palms run.
> From this we could get 7 divided by 5 ½ = 1.272727
> however if we say 1 divided by 5 ½ we get .181818
> so as we see not the correct ratio.
> You could double the palms to 14 rise and the run
> to 11 palms however if you doubled the 1 cubit to
> 2 and then doubled the 5 ½ palms to 11 you would
> end up with 2 divided by 11 = .181818 so not the
> correct answer. During construction of the G1 core
> blocks very few levels correspond to whole number
> of cubits or palms so I would lean towards them
> using digits not palms or cubits in rise to find
> the horizontal run needed.

Hello RLH,

It is a fact that the AEs defined a seked as: 1 [Royal] cubit rise to X palms run.
As far as is known, the AE pyramid builders did not measure gradients in degrees, minutes and seconds.
If somebody today wants to know what a particular seked is in degrees, minutes and seconds, then their first step is to convert the 1 royal rise to 7 palms – obviously, one cannot divide 1 royal cubit by 5½ palms; it has to be a case of 7 palms divided by 5 ½ palms.
If an AE wanted to know a pyramid’s seked from its height and half length of a side, then he would have needed at some point to convert rise 1 royal cubit to 7 palms to carry out the calculation (in the Rhind Mathematical Papyrus there are examples of this happening).

> During construction of the G1 core
> blocks very few levels correspond to whole number
> of cubits or palms so I would lean towards them
> using digits not palms or cubits in rise to find
> the horizontal run needed.

As I have previously stated, I hypothesise that the seked was also seen by the AEs as 28 digits rise to X digits horizontal – particularly in the case of the planning of the Great Pyramid.
It is clear from the EMP that though a seked was defined as 1 royal cubit rise to 5½ palms horizontal run, when it came to calculations it was seen needfully as 7 palms rise to X palms and (possibly) X digits horizontal run.

Please see the extract from Rossi’s ‘Architecture and Mathematics in Ancient Egypt’ I posted in this thread earlier.
As I have previously stated, I hypothesise that in the case of the planning of the Great Pyramid the seked was seen as 28 digits rise to 22 digits horizontal run.
On perhaps a fairly minor point, it is not clear (to me, at least) how a horizontal run that included a fraction of a palm was usually seen by the AEs.
For example, was it 5 palms 1 digit or 5¼ palms?

> There is the possibility they had a wooden
> template pre set at seked 5 ½ and no actual
> measurement of run was needed for each core block
> level.

I think this highly likely, and my impression is that most Egyptologists think the same.

> Just some thoughts on my part and no
> offence intended.

RLH, I detect not the slightest offence in your post.
I had not explained at all well the differences involved in the AE definition of the seked and calculations involving the seked (i.e. the need to convert the royal cubit rise into palms [or digits, as the case may be]), and I appreciate your pointing this out.
Hopefully, I have now made clear the situation as I see it.

Regards,

MJ



Edited 1 time(s). Last edit at 10/30/2011 11:01AM by MJ Thomas 2.