Hermione Wrote:
-------------------------------------------------------
> MJ Thomas 2 Wrote:
> --------------------------------------------------
> -----
> > Anthony Wrote:
> > > Nice try, but none of it is actually a logical
> > > rebuttal in any way to the facts I presented.
> >
> > Well, you're quite right about 440/280 (and
> > variations of) not equalling 22/7.
> > But you have not addressed any of the questions I
> > put to you about your doubling 220 to 440, the
> > base having four sides, etc.
> > Why not?
>
> MJT to AS:
> >you baulk at the idea that the AEs could have
> gone for half the perimeter divided by the height,
> or the perimeter of the base divided by twice the
> height.
> >Why?
>
> Because that's just cherry-picking dimensions to
> prove a case, isn't it ...
Hello Hermione,
I don’t think so.
The length of the side at the base was always (as far as is known) seen as twice the horizontal distance between the apex of the pyramid (or the centre of the square base) and a side at the base.
In the Egyptian Mathematical Papyri (EMP) there are examples of doubling and halving being used necessarily to calculate a pyramid’s height and or base and or seked.
A pyramid’s height was normally either a) a voluntary choice or b) the natural product of a voluntarily chosen base and seked (which raises a key point about the seked in Khufu’s pyramid, but more on that later) .
Its height is naturally a highly integral part of a pyramid, so I do not see recourse to it as cherry-picking.
If I were to call on, say, the length of the Descending Passage instead of the pyramid’s height, then that would, IMO, be cherry-picking a dimension to suit my argument here.
Seked 5½ produces naturally in a pyramid the phenomenon: the height of the pyramid is to the perimeter of its base as the radius of a circle is to its circumference.
I see no real reason to suppose that the AEs never thought of a square or rectangle in terms of its perimeter.
As my example in my previous post hopefully demonstrates, the AEs were quite aware of both diameter and radius.
Having said that, I need to keep in mind that as there is no mention of circumferences in the EMP, so there is no mention of perimeters (AFAIK).
But, then, this needs to be balanced against the fact that in the side (north and south) walls of the King’s Chamber we see the phenomenon: the length of the wall is to its perimeter as the diameter of a circle is to its circumference.
> To be persuaded that
> the GP really encoded some esoteric reference to
> 22/7 (whether such a ratio was actually recognized
> as pi or not), I think that most people would be
> looking for the total measurement of the perimeter
> of the base divided by the height to produce the
> required quantity. But 440 x 4, as we know, is
> 1,760 ... and, divided by 280, all you get is app.
> 6.29, or 44/7, or 2 x 22/7. Why on earth would
> anyone, ancient or modern, use half the perimeter
> only in such a calculation... ? It just makes no
> sense ...
IMO it only makes sense as: the height of the pyramid is to the perimeter of its base as the radius of a circle is to its circumference.
I much prefer this to:
the height of the pyramid is to half the perimeter of the base as the diameter of a circle is to its circumference
or
twice the height of the pyramid is to the perimeter of the base as the diameter of a circle is to its circumference.
If Khufu’s architect used multiplication and division by 22/7 to determine precisely some of the Pyramid’s dimensions (and, as you know, I firmly believe that he did), then it was not, IMO, meant to be as “an esoteric reference” of some kind.
I believe that the architect used 22/7 simply because it appealed to him or – perhaps more likely – his king.
Whether or not this appeal had something to do with the relationship between 22/7 and circles is impossible to say, but IMO that it was is quite possible.
I don't think we need to invoke the occult, etc.
MJ
Edited 1 time(s). Last edit at 06/27/2009 12:52PM by MJ Thomas 2.