Slefold
Wykehurst Lane
Ewhurst
Surrey GU6 7PE |
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26/5/79 |
Dear Mr. Goodfellow,
Many thanks for your interesting letter about the Giza
Pyramids. We seem to agree that these structures were not
originally built as tombs; although I am sure that they
were used as such during the IVth Dynasty; and I happen
to think that the great majority of pyramids - including
Sekhemkhet's, by the way - were built for that purpose.
The wall-paintings you mention really belonged in the
adjoining temples... However, barbarian though I may be,
the idea of finding the intersections of circles
enclosing the three pyramids of Giza, had never crossed
my mind before reading your last letter. I had previously
given some thought to the smaller of the two ground
circles, but the larger one, passing through the S.E.
corners, is so disproportionate with its q km. radius,
that I rather doubt whether the architect could have
accurately drawn it in the way he would have wanted to,
on a scale plan of reasonable dimensions. On the other
hand, he may have known that the centre of a circle lies
at the inter section of the perpendicular bisectors of
the chords, and could conceivably have calculated a
solution on that basis.
Now as you say, any three points make a circle - even if
they are aligned, as some would have it. But since the
three pyramids are separated by axial distances in a
logical extension of the square bases, and all the
dimensions are simply accounted for in this way - the
enclosing circles, and their points of intersection, are
in my view unlikely to have been controlling factors in
the design. At the same time, point of intersection were
produced and may have been of interest to the builders -
but I would be suprised if the dimensions were at all
significant.
As to the intersection of the circle passing through the
three apexes, I really think that you should abandon this
idea. I see no reason for neglecting the different levels
of the three pyramid-bases, since the builders were well
aware of these and would without doubt have taken them
into account. However, the apexes will be shifted by so
much that I don't think there could be any chance of a
common intersection with the ground circles. Also, which
of the three bases is to be chosen -as the ground level -
or perhaps one should find the mean level of the three,
or the level of the ground where the circles meet?
Just to set your brains rattling, I enclose a copy of the
only data I have of the different levels, taken from
Vyse's "Operations carried on at the Pyramids of
Gizeh in 1837", Volume II. You will find that the
apex of the Second Pyramid is actually higher than that
of the Great Pyramid, while the Third Pyramid is likewise
raised 40 feet or so. I find it hard to imagine that the
architect would ever have attempted a three dimensional
trignometrical solution for the intersection of these
circles. The plane of the circle through the apexes is
not, of course, vertical, but tilted at some large angle
to the horizontal - something that I would definitely
prefer not to contemplate.
After a number of years of sharpening my wits under
pyramids - as it were - my present intention is to try
and preserve them. So although I would be happy to
confirm or disprove your theories when these are based on
level ground, any particularly mind-boggling mental
exercise is not going to take my fancy. Thus I might try
working out the numbers but for the two ground circles
only. I would, however, be interested to know what you
are expecting to find from digging at a spot which, from
the photos I have of the area looks like a pretty barren
stretch of desert?
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Yours Sincerely,
John Legon |
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