Now with regard to the dimensions of these circles, I had
always taken the view that they were coincidental by-products of the Giza Site
Plan, without any real significance of their own. After all, it seemed highly
unlikely that the architect of the site plan could have calculated the radii and
the centres, let alone have configured the layout to obtain specific results. In
any case, I had already ascribed the exact dimensions and relative positions of
the three pyramids to a highly logical and coherent design, in which every
measurement had been explained and often with reference to more than one
requirement. There was little reason to think that any further factors had to
be taken account - least of all two circles of enormous size.
However,
there was a nagging suspicion that my preconceptions were not entirely
justified. From the outset, one or two of the dimensions were clearly
significant, as I mentioned to Stephen in a letter many years ago. It was
exceedingly strange that the centre of the large circle was just 11,000 cubits
southwards from the vanishing point itself, with a computed discrepancy of only
0.13 cubit. Not only did the chances of randomly obtaining such a round number
with such accuracy seem rather slight, but the number was significant in its own
right. In the Giza plan, as we have seen, the modular design placed the south
side of the Second Pyramid 1100 cubits southwards from the north side of the
Great Pyramid, so that the north-south dimension encompassing these two pyramids
was just 5/2 times the base of the Great Pyramid of 440 cubits. In addition,
the coordinates of the vanishing point and the radius of the small circle
corresponded to whole numbers of cubits to within 0.05 cubit, and although not
particularly interesting, conformed to the cubit system.
It was only
recently, however, that some further relationships came to light, when Stephen
pointed out that the circumference of the large circle was just 20 times the
diameter of the small circle. The exact factor of 20.04 was close enough to a
round figure to suggest deliberate intent. Now for the reasons outlined above,
I hadn't paid much attention to the dimensions of the circles, and cannot recall
having calculated the circumferences. I knew that the radius of the large circle
corresponded to a round 17,500 cubits, with a discrepancy of only 0.04%, but had
declined to draw any further conclusions. The diameter of the large circle is,
however, practically just 35,000 cubits, so that given the approximation to
p of 22/7, the circumference will be 110,000
cubits. Not only is it inherently quite surprising to obtain these simple
multiples of 10,000 cubits, but the circumference is also just 10 times the
distance northwards from the centre of the circle to the Vanishing Point -
through which, by definition, the circumference must pass.
Once again,
therefore, it is not just the whole numbers of thousands of cubits which are
significant, but the fact that these dimensions are mathematically meaningful.
Being a multiple of 7000 cubits, the diameter of 35,000 cubits would have been
an ideal choice - if indeed it was chosen - since the circumference would also
contain a round number of thousands of cubits, according to the 'classic' value
for p of 22/7. The same reasoning applies
also to the Great Pyramid, which is thought to embody the
p-proportion through its height of 280
cubits and side-length of 440 cubits. Furthermore, the circumference of the
large circle is just 250 times the side-length of the Great Pyramid, and the
dimensions of 440 and 250 cubits are consecutive in the Giza plan.
It
must be noted that the diameter of the large circle is highly sensitive to the
exact placing of the pyramid corners through which the circumference passes,
owing to the flatness of the curve which connects them. Indeed, if the three
corners had been placed in a straight line, then that line would belong to the
circumference of a circle with infinite radius. Although the slight bend in the
line reduced the diameter to a 'sensible' dimension, the dimension changes
rapidly with slight adjustments of the pyramid corner positions. It turns out -
and I still find this hard to believe - that the precise diameter of 35,000
cubits can be obtained for the large circle by shifting the south-east corner of
the Second Pyramid a mere 0.006 of a cubit from the position as defined by the
site-plan coordinates in whole cubits!
If it had ever been intended to
define a circle with a diameter of 35,000 cubits by means of the three
pyramid-corners, therefore, then it would have been virtually impossible to
achieve a more accurate result than that actually obtained by the site-plan
dimensions. It is true that the circumference of the circle will not be exactly
110,000 cubits if the exact value of
p is used instead of 22/7, yet the
relationship with the Great Pyramid still stands, since the dimensions of this
pyramid arguably reflect
p with greater accuracy than 22/7.
Now
turning to the small circle, my computations had shown that the radius was 2742
cubits, while the centre was 2740 cubits eastwards from the Vanishing Point.
This number was significant to me as being practically ten times the height of
the Second Pyramid, which the survey-data and theoretical factors had shown to
be 274 cubits. Whilst the dimensions of the large circle seemed to refer to the
Great Pyramid, therefore, a comparable relationship existed between the small
circle and the Second Pyramid. At the same time, the diameter of the small
circle is a fair approximation to one-twentieth of the circumference of the
large circle, as Stephen suggested - this requiring a radius of about 2748
cubits.
The Boundary Wall We have already referred to the
anomalous boundary wall to the south of the Third Pyramid, which seems to run
straight over the Vanishing Point. Stephen wanted to know whether the wall
described a large circle, and whether it was possible - given the fragment that
exists - to accurately determine the size of the circle. It might be
interesting at this point to quote from a letter I sent Stephen on 16th April
1987: |