L Cooper Wrote:
-------------------------------------------------------
> Ronald wrote;
>
> "The "squaring the circle" arguments are a product
> of modern minds. One has to try to replace
> her/himself into the mind of the Ancient
> Egyptians. These people certainly did not think
> within the concepts of maths we have today. There
> also was simply no need to do so. I retain my view
> that you do not need much 'math' (what's in a name
> ?) to build tens of quadrangles of diminishing
> size on top of each other (limestone-block
> courses) to achieve a pyramidal shape."
>
>
> I agree with you that the ancient Egyptian
> "concepts of maths" were different from that of
> today, and that it is important to make the
> attempt to enter into their ways of thinking and
> world view. I absolutely and totally disagree,
> however, that the "squaring of the circle
> arguments are a product of modern minds". I find
> this statement somewhat stunning in light of the
> Egyptian method for finding the area of a circle.
> Given problems 48 and 50 of the RMP (not to
> mention MMP 10), it is not clear to me what level
> of proof one would want in order to accept that
> the Egyptians squared the circle in terms of area.
> (Gillings refers to the scribe of the RMP as being
> "the first authentic circle-squarer in recorded
> history").
>
> Note that I am not saying here that the Egyptians
> thought of things in terms of Pi, as we might do
> today. I believe their conceptual approach in this
> situation was a diagrammatic - or graphic - one
> (Peet uses the word "graphically" to describe the
> Egyptian method used in MMP 6). Friberg, in his
> Unexpected Links Between Egyptian and Babylonian
> Mathematics, exposes much of the geometric
> underpinnings of Old Babylonian mathematics (his
> term for their methodology is "naive geometry"),
> and after extensive comparisons between OB and
> Egyptian mathematical texts comes to the
> conclusion that "Middle Egyptian and OB
> mathematics must have influenced each other in
> decisive ways" (p. 103). He implies that the
> Egyptians likely also thought "graphically" when
> dealing with certain mathematical situations. (As
> one instance, he points to P. Berlin 6619, showing
> that in computing square roots, the method
> involved the computation of "squaresides, that is
> sides of squares". p. 82)



>
> I have gotten the sense from some of the
> discussions here that there is a view that the
> ancient Egyptians were, in certain ways, a bunch
> of simpletons,


Lee,


Of course the AE were no simpletons ... As far as I'm concerned, I see the AE mainly as intuïtive builders, not as builders regularly using maths.


Maybe Anthony is going to shoot me for this, him being a convinced supporter of the planned pyramid. I am pretty convinced you do not need much planning to lay extended courses of stone-blocks from the moment you have measured/laid the base quadrangle. The planning begun when these courses reached the location of the core, thus the overground cavities in e.g. the GP (DP, AP, Queen's Chamber, GG, King's Chamber, releave chambers, shafts). This core is very small, compared to the overall mass of the pyramid. Seen from above, it only represents a really thin line in the middle of the mass. Thus, the part that really needed planning was very small. Also the cutting/construction/placement of the casing-stones must have been carefully planned.


Ronald.