Tomb Engraving &
The Golden Section
The below arrticle is really interesting in that it contains certain
findings I made in 2007, which it seems, might have been made by a
Russian architect long time before me. I can't be sure of
exactly how the other work goes, because it is onily available if you
buy the book. I don't buy such books out of principle just like I don't
try to make anyone pay for the information available here.
The Graven Image of Hesire
wooden door in hs tomb is almost 47 centuries old. Like
Imhotep, architect of the first pyramid in
Egypt, Hesire belonged to King Djoser's (Zoser's) intellectual
elite, and held many titles
like Overseer of Scribes, and Chief
In this image, Hesire grips two staffs in such a manner that they
form a right angle. The upright staff looks
approximately twice as long as the level one. If there is a clue that the image is constructed on
a geometric basis, this is it. At the same time, Hesire looks not
unlike a warrior 'en guarde' with a sword, and a
shield . Indeed, these weapons refute those
Egyptologists, and historians, who uphold the present
consensus that ancient Egyptians had only rudimentary
knowledge of mathematics, their value for Pi was about 3.16, and they
didn't know and use the Golden Section. Yet, the truth is that
Egyptians had considered the Golden Section sacred, and thus perfectly
suitable, one could say a must, for the planning of their
temples and tombs. We have seen, how extensively the three Giza pyramid
temples embody the Golden Section.
To put the clue to
a test, the length of the upright shaft serves as the basis for two
side by side squares. The diagram below shows that the testing
squares fit the figure. For example, the
line dividing the rectangle into two squares is also a line of
of Hesire's sword
along the lower edge of Hesire's 'sword' gives the Golden Proportion with
the (parallel) central axes of both squares in the column.
When we fit two golden rectangles below the top of the lower square, as
in the image, or when we center a golden rectangle in the middle of the
two-square column, in the process, we recreate the lower edge of
the engraved clue line.
A natural progression of experiments
right foot meets the ground at a perfect right-angle, it
provides an experimental socket for the two-square column from above.
First, we just transport the column to the socket to anchor it
there without changing its angle. In this case, the left side
of the column shows definite alignment with Hesire's body. The yellow
lines in the diagram below are those of the Golden Section. The Golden
Section line on the right runs with the edge of the long staff. On the
other side the equivalent line runs to Hesire's eye. There are other
harmonies. One diagonal of the top square runs with the edge of
Hesire's forearm for most of its length. The top side of the column
limits hesire's left shoulder at the armpit.
All details considered, this experiment
also shows some merits, and yields further
insight into the designer's methods.
obvious next step
Next, the anchored
column is aligned to Hesire's foot. The result is more harmony between
Hesire's figure and geometry. For example, a different
golden-section line now passes through the same corner of
Hesire's eye. Notably, the column in this position determines the
limits of Hesire's figure on two sides, the bottom, and the right.
This leads to an idea that these two limit lines are like half a bounding box (frame) for the figure, and so, completion of this bounding box is the
subject of the (for now) final experiment.
The short staff
sets the width of the bounding box (the frame) on the left. The top
side is then added automatically. This is a standard experiment, in
which three rectangular lines form a socket for corresponding figures.
We can insert a square, or golden-rectangles, or their
combinations into the socket. If the designer had worked with
the Golden Section at all, then these experimental expansions make it
possible to fall in tune with the original design.
Hesire's frame can
be seen in several ways - a square sandwiched between two horizontal
golden rectangles, or two stacked golden rectangles,
one vertical, one horizontal. Careful scrutiny of the result
reveals much harmonious correlation between the image and the grid. For
instance, the vertical limit line on the left of the previous column is
also incorporated into the new grid, and so is the top line of Hesire's
Conclusion: The designer of Hesire's image on the wooden door in his
tomb had deliberately integrated the Golden Section in
August 8, 2007
Note: The rasterization module in my
vector driven program has a stubborn kink, which elongates
the rasterized images vertically by about three and a half percent
(1.034 to 1.035). This is a recent problem, dating from "The
Giza Pyramid Temples & the Golden Section. I am not willing to
readjust raster images, it just does not seem right. But, such
adjustment will produce the optically correct ratio.