# The Giza Vanishing Point
Here is a link to Stephen Goodfellow's
Giza Vanishing Point web site.
Click here for an Update -
September 2005
Back in 1979, just as I was about to have my
findings on the Giza Site Plan published for the first time, I was contacted by
the Detroit artist Stephen Goodfellow. Evidently, Stephen had attended a lecture
given in the US by the Egyptologist Robert Anderson, who was then Honorary
Secretary of the Egyptian Exploration Society in London. For reasons best known
to himself at that time, Stephen had asked Robert whether he knew of anyone who
could supply him with accurate information about the dimensions and relative
positions of the three major pyramids on the Giza plateau. It so happened that
through the EES, I had recently shown some of my work on the Giza plan to Mr
Anderson, who was therefore aware that I had carried out a detailed analysis of
Petrie's survey results for the Giza monuments, and had calculated the exact
dimensions and relative positions of the three pyramids in terms of the
customary Egyptian units of measurement.
By this rather far-fetched
coincidence, Stephen was put into contact with one of the few people anywhere
who could provide him with precisely the information he was looking for, in
order to investigate his concept of a "vanishing point" for these
three famous pyramids. Stephen had the idea that the three pyramids together
could be encompassed by inner and outer circles, which would intersect at a
single point comparable to the vanishing point used by artists to define the
visual convergence of parallel straight lines. Whilst the successively
diminishing dimensions of the three pyramids could not be explained by the
convergence of straight lines, any three points in a plane can be shown to fall
on the circumference of a circle, and hence it was possible to construct circles
which would pass through the SE and NW corners of the three pyramids, and
intersect at a single point comparable to the artist's conception of a vanishing
point.
As I recall, it was seven or eight years before I agreed to
carry out the detailed calculations which Stephen had asked for. I had always
taken the view that the plans of the Giza pyramids had been based primarily upon
rectilinear geometry - the use of straight lines and right angles - and it
didn't seem to me that there was much evidence to suggest that the architects
had made use of circles in their designs. Furthermore, the encompassing circles
of the Giza pyramids are of very large dimensions, and it was absolutely
inconceivable that these circles could have been laid out on the ground. If
Stephen's concept of a vanishing point for the Giza pyramids had any validity
whatsoever, then it was only by calculation that the pyramid-architects could
have determined this position on the plateau, and for this they would have
required some basic knowledge of the geometry of the circle, as well as an
understanding of Pythagoras' theorem.
Perhaps it was my developing
interest in computer programming that made me respond to Stephen's renewed
request that I should calculate the exact position of the Giza vanishing point.
With the fairly new-fangled contraption of the home computer, I could compute
the dimensions and points of intersection of the various circles that can be
passed through the corners and centres of the three pyramids, with great
precision and in a relatively painless manner.
The results of these
calculations proved to be rather more interesting than I had anticipated. For
the vanishing point turned out to be located not on some empty patch of desert,
but very close to the stone enclosure wall situated to the south of the Third
Pyramid. At first glance, this position did not seem to be very promising; yet
I knew that the most significant archaeological discovery at Giza over the past
seventy years had come about after a similar enclosure wall had been demolished
- this wall having been built on the south side of the Great Pyramid, on top of
the roofing-beams of the rock-cut pit in which the disassembled wooden
components of the fabulous Cheops boat were discovered.
I was also
puzzled by some curious features of the enclosure wall on the south side of the
Third Pyramid. Whereas the walls to the north and west had been laid out on a
plan conforming rigorously to the cardinal directions from east to west and from
north to south, the wall on the south side of the Third Pyramid veered away
towards the south, and had a curve of enormous radius, reminiscent of the
circles which encompass the three pyramids. At one point along this curved wall,
furthermore, a short branch wall had been constructed towards the north in two
segments, which resembled the chords which I had drawn between the
pyramid-corners in order to define the dimensions of the corresponding circles.
These
factors, taken together, have led me to the conclusion that there might be some
merit in Stephen's vanishing point theory. Although I still maintain that the
dimensions and relative positions of the Giza pyramids were determined by the
design which I first described in 1979, the concept of the vanishing point could
be said to represent the summation of this design, since the exact spot depends
upon the positions and dimensions of all three pyramids together. Perhaps one
day, the enclosure wall will be properly excavated and something of interest
will come to light. Or perhaps not. Who knows?
John Legon, 27/5/2000 |