Sirfiroth Wrote:
> We see pi because that is what we were trained to
> do, never dreaming of a world without pi, or any
> other possibility.
We see the pi ratio (usually as the approximation 3 1/7) in the Great Pyramid's superstructure and the side (north and south) walls of the King's Chamber for the simple reason that they are there (within a fraction of an inch).
The question is: is there presence deliberate or natural?
Answer: we don't know.
And this is how the true situation will remain until such time - if ever - the original plans of the Pyramid or some equivalent original text turn up - but this is no reason not to speculate on what was intended.
I am convinced that multiplication and division by 3 1/7 (or a single equivalent thereof) was used extensively in the planning of the dimensions of Khufu's pyramid, its passages and chambers, and their respective features (e.g. King's Chamber sarcophagus, Queen's Chamber Niche).
Unfortunately, I cannot say what this number (or some equivalent value) was or what it meant to the Pyramid's architect.
However, if push comes to shove, then my money is on the diameter-to-circumference ratio we all know and love as pi and usually see as the approximation 3 1/7.
True, this ratio does not appear in the Egyptian Mathematical Papyri (EMP), but this does not mean that the Ancient Egyptians were not aware of it; after all - and as mentioned by RLH - it is very easy to find the length of a circumference with a rope and a measuring rod.
AFAIK, there is no direct reference to the measuring of the perimeter of a square or a rectangle in the EMP.
Are we to assume from this that the Ancient Egyptians did not know that the perimeter of a square is 4 times the length of a side, and the perimeter of a rectangle is twice the length plus twice the breadth? - I don't think so.
It is argued by some that if the pi ratio of whatever value was used in the planning of Khufu’s (or anybody else’s, come to that) pyramid, then it would have had some religious/magical/spiritual meaning and or significance and would therefore appear elsewhere in Ancient Egyptian structures and, more to the point, texts such as the Pyramid Texts.
That it doesn’t is seen as proof (again by some) that the Ancient Egyptians were unaware of it, and therefore it cannot have played a role in the planning of any pyramid or other structure.
The question is, of course: why should the pi ratio have to have had a religious//magical/spiritual meaning and or significance in order to be used in the planning of a pyramid?
We don’t expect the perimeters of squares and rectangles to have had any such significance, so why should the diameter-to-circumference ratio be treated any differently to this?
Perhaps the Ancient Egyptians did not hold the pi ratio in such high regard as we today tend to do.
Perhaps its use in the planning of a pyramid was all down to the whims and fancies of the king for whom the building was intended.
MJ