 
3. GEOMETRIC DESIGN OF
THE "GRANITE LEAF
AND THE "BOSS"
The following is my proposal to
demonstrate that the granite leaf slabs and its carved boss over the north side
of the upper section, are a result of the same type of geometric pattern
configuration, and that this configuration corresponds to the configuration I
suggested for the solution of the Great Pyramid's geometry in my previous posts,
and to design, build, and seal the antechamber.
The shape and
dimensions of the boss are shown below:
The boss was defined by Sir W. Petrie to be a rough carving over the side of the
granite leaf stone, as other similar carvings over the sides of the stone
blocks, used to handle and manipulate these stones blocks for the building of
pyramids, tombs and temples.
My idea, for many years, is that this particular object do not represents a
working boss. To apply a label of a working boss, because all bosses are carved
over the stone surfaces in a similar way, is not enough for me to conclude that
this is a working boss. There are other factors to be considered. However, I
look at this carved object as a "key" to the pyramid's design, included by the
pyramid's designers as their signature. In its design, their use the Perfect
Symbol, but we have to know it to discover its use. It is probable that the
engineers gave us the secret of the pyramid's design at the time they give us
the carving.
The following sequence of drawings shows a summary of the boss's design.
I used the Perfect Symbol to explain the geometry involved in
the design of the Great Pyramid.
 to explain the geometry involved in the antechamber design.
 to explain the geometry involved in the pyramids of Chephren, Mycerinus,
Bent, Read, and many others.
 to explain the geometry involved in
Leonardo da Vinci's drawing for the human body proportions.
 to explain the Pyramid's layout Plan in Giza.
 to explain the reasons and construction of the boss.
 to explain the Pyramid's ventilation shafts design.
 to explain many important
architectural drawings of buildings.
 Therefore, the Perfect
Symbol should be studied and evaluate for its characteristics and properties
leading to more discoveries.
As a brief review of the use of this configuration in the Great Pyramid, the
radius of the circle represents the Pyramid's height. The triangle (QHT) represents the cross sectional view of the Great Pyramid, as be seen through a
vertical plane cut though the center of its faces. The square joining points I,
II, III and IV, symbolizes the square base of the pyramid, as projected in the
vertical plane of the cross sectional view of the pyramid. The base (PN) of the
large triangle (PQN), divides the vertical diameter into two sections, QX and XK,
at the point marked as X. The location of point X is very important and
represents in the Great Pyramid, the point where the two sections of the
vertical diameters have a ratio equal to Phi (1.618).
Besides, point X is where the descending passage line will arrive at the pyramid's axis. This is the
most important point in the whole configuration, being suggested by me as the
possible location for the pharaoh's mortuary chamber. Since the plane of this
drawing is through the center of the pyramid and the vertical axis, this point
would be located to the west side of the center of the horizontal passage leadin
to the subterranean chamber (22 ft). The proportion
between the two sections (QX / XK) is equivalent to the golden section number,
that is, 1.618, number which is called Phi value. In this
configuration, the two sections could be exchanged and the point called X will
be relocated over the pyramid's base, at the same vertical distance it was
located below the center of the pyramid.. I called this Phi point over the horizontal diameter as point X'.
This proportion would be (X'K / QX') = 1.618 (Phi). If you set the radius of
this circle equivalent to the pyramid's height, and calculate the complete
configuration, you will see that the dimensions, are the same as found in the
Great Pyramid.
The next figure shows the location of the Phi point in the vertical diameter,
point X, and point X', since the figure of the pyramid could be inverted.
However, point X can be exchanged with point X', and still represents the
division of the vertical diameter into two sections, having a ratio equal to
Phi. As indicated, this would be my other suggested location where the Pharaoh's
could have selected to build his (not found yet) mortuary chamber.
As I stated, this geometric configuration help me to develop the Giza's pyramid Layout,
where the combination of the diameter of the circle and the square base
measurements of the Great Pyramid gave me the numbers to automatically, set up
the dimensions of the huge rectangular area where the three big pyramids are
enclosed.
In Leonardo's drawing, this geometric configuration confirms the attributes he
gave to the proportions of the human body figure, and shows that the design
pattern he used for the drawing is just a section generated by this
configuration.
In the boss shape, the geometric configuration denotes the way to trace and
carve such a difficult shape, in a simple way, giving us a perfect carving in
accordance with its dimensions. Its shape is a representation of the geometric
configuration.
At this time I will present the same geometric configuration to design the
granite leaf of the antechamber. Remember, all these studies are not the work of
days, months or several years. It represents the work of over 3 decades.
However, to design the granite leaf, took me less than one week, after my
experience with the antechamber and my search for the meaning of the "boss".
Afterwards, it came to my mind, if the carved object was design using my
developed geometric configuration, the designer must have certified his work by
using the same configuration to design the granite leaf. So, I explored this
possibility, and I was astonished by the findings.
Please observe that I am going to design the granite slab using no numbers, no
proportions, no calculations, etc. The only number I am going to set in the
configuration is the radius, or diameter of the draw circle. All calculations,
when the drawing is finished, will correspond to the dimensions as fixed by the
circle's diameter in the geometrical process. This is exactly what I did for the
Great Pyramid's geometry, and apparently has been difficult to be understood by
many. Maybe this simple stone slab, will show more clearly what I meant.
The following figures show the sequence to design the granite slab. I have
setup the width of the antechamber (east  west) as being 65.60 inches. Sir W.
Petrie indicates that its width varies from 64.48 to 65.48". However, the
difference of 0.12 inches makes no difference. I can be neglected; therefore, I
set the diameter of the circle equivalent to 65.60 inches. Observe that the
design method will be exactly the same I used for the design of the boss.
Let's say that the designer decided to use the geometric configuration and set
the square section shown between points I, II, III, and IV, as the basis for
designing the granite leaf dimensions (this square corresponds to the base of
the Great Pyramid in that analysis). In other words, the square will represent,
initially the granite slab frontal view.
Since the circle's diameter has been fixed as 65.6 inches, we can start the
calculations. For this, I use at present time my computer's program, which gives
me, immediately, the results in the desired unit of measurements.
As it is shown in the following figure, the sides of the square are calculated
as 51.57 inches. However, the designer wants a rectangular shape for the granite
leaf, not a square. So, as he did for the design of the boss, he traces a line
from the center O, perpendicular and to intercept the inclined side of the
pyramid, and mark point W, at the intersection point.
Using line (OW) as a radius, he traces a circle where its circumference would be
tangent to the inclined sides of the pyramid. The two intersection points of the
circumference with the horizontal diameter are marked S and Y. We have done this
before for the boss figure design.
At points S and Y, draw vertical lines, which will exactly intersect the points
at which both the interior circumference and the sides of the square are joined
together.
Therefore, we have created a rectangle 51.57 inches height, and a width which is
equivalent to the distance SY = 40.54 inches. The two vertical rectangular areas
to the sides of the center rectangle measure 5.51 inches width and have a
vertical height of 51.57 inches.
Now, take a look to the section of the circumference of the circle that
establishes the point X', above the horizontal diameter. This point X', which
represents the Phi point in the diameter, was calculated to be located,
vertically, at 7.74 inches above the horizontal diameter, as shown in the
following figure.
The figure shows that the granite leaf is 51.57 inches height and 40.54 inches
width. Since point X' is equivalent to 7.74 inches, it is located at 25.06 inch
from the top of the circle (32.8  7.74) = 25.06 inches, while the other segment
of the diameter measures (65.6  25.06) = 40.54 inches to the bottom of the
circle. This means that the ratio 40.54 / 25.06 = 1.618 = Phi proportion.
Therefore, the location of point X', represents the Phi point, above the
horizontal diameter.
The location of point X, when dealing with pyramids seems to be very important.
Therefore, many years ago I developed a formula to locate this point for any
type of square base pyramid, no matter its configuration. My formula states that
the distance from the center of the base of the pyramid, to either point X, or
X' = OX = (4  k ˛) R / (4 + k ˛), Where k ˛ = (b / R). The center of the base
is O, the base length of the pyramid = b, and the radius = R = pyramid's height.
As an example, let's see where this point would be located for the Great Pyramid
(assumed: Height = R = 480.66', b= 755.75).
X = [4  (755.75 / 480.66) ˛] (480.66) / [4 + (755.75 / 480.66) ˛] = 113.47 feet
below the center of the base and in the vertical axis.
This is the same vertical distance, from the base and center axis of the
pyramid, up or down, which I stated the Pharaoh's mortuary chamber could be
located if he used this configuration for his pyramid.
However, this particular geometric configuration, gives us an alternative for
this calculation (not the same for other pyramids). The vertical distance OX is
also equivalent to the pyramid's height divided by Phi cubed. In the Great
pyramid it would be 480.6637 / phi cubed = 113.47', which gives the same result
we have already calculated with the formula.
Now, going from the huge Great Pyramid to this small stone slab, the distance to
point X', shown in the design, would be: Assuming R = 65.5 / 2 = 32.75", b =
51.57"
X = [4  (51.57 / 32.75) ˛] (32.75)] / [4 + (51.57 / 32.75) ˛] = about 7.7
inches. However, using the short formula for this configuration, where OX =
pyramid's height / phi cubed, we have 32.75 / Phi cubed = 7.74 inches, which is
a more exact calculation. This is the same result I got using the computer.
Therefore, it has been determined that point X', which is the most important
point in the whole configuration, would be located at 7.74 inches above the
center of the base of the small pyramid shown in the drawing. The importance of
this calculation will be seen in a moment.
Since this point X' is so important, and if I were the designer, in order to
show that I meant something more, than a simple boss, with the carved object, I
would place it exactly over the X' location. This is the same procedure I would
do with the Pharaoh's mortuary chamber, placed it over or under the pyramid, but
in this point. I have written a whole chapter dedicated to this point and its
numerous interesting characteristics.
Anyway, doing this, the designer will prove to the no believers, that certainly,
the message is there, it should be clearly understood by researchers. This will
constitute evidence to prove that it is not a construction boss. The chances of
being here a construction boss could be one in millions.
At this time, I will draw at and exact scale, over point X', the drawing of the
carved object.
As it would be observed, the carved object was placed exactly over point X,
which represents the Phi point in the vertical diameter. Placing the boss at
this location, we get the dimensions shown in the drawing for the granite slab.
However, the designer wanted to finally define the granite slab width. He will
keep the height of 51.57 inches. He wanted to prove that he intentionally set
the boss in this place. To do that, he set the width of the granite slab, by
extending the vertical distance from the top of the pyramid to the center of the
boss (the vertical and horizontal center of the designed boss). Therefore, there
is no doubt about the boss location.
Please, keep in mind that all this numbers are a result of the geometric
process, based on a diameter of 65.60 inches for the circle. The process
generates all these measurements. As it can be notice I have not use any of the
granite leaf actual dimensions here, just the antechamber's width, as the
circle's diameter.
The center of the base of the carved object was placed exactly at the Phi point,
which is located at 7.74 inches above the horizontal center of the slab, as
stated. To define, for all to see, the real width of the slab, a circle was
traced from the upper section of the diameter (point Q) to the center of the
boss (24 inches radius), which set the width of the slab as 48 inches. In order
that everybody could understand his message, the designer set the upper granite
slab as 24 inches height, which represents the vertical distance from the top of
the pyramid to the center of the boss.
Therefore, the boss lower boss section would be located 6" above the rim between
the two granite slab sections. In all, since the boss is 6" from the rim of the
two granite slabs, plus the 5 inches height of the boss, and the 13.00" from the
top of the circle to the top of the boss, it makes the 24 inches height. The
vertical distance between the rim o the two slab sections and the center of the
slab = (51.57 / 2)  24 = 1.788 = 1.79 inches.
I have designed here a granite slab, which resulted with the dimensions shown in
the next figure, using only the width of the antechamber (65.6 inches). I did
exactly as for the design of the Great Pyramid and all its corridors, passages,
chambers, etc. at that time using only the pyramid's height (480.6637). All
thanks to my geometric configuration, which is only applicable to the Great
Pyramid and all its sections.
The references shown below set the granite slab and boss dimensions as follows:
1. Width of the slab = 48"
2. Height of the slab = 51.57"
3. The upper section height = 24"
4. The vertical distance from the bottom of the upper slab to the lower section
of the boss = 33.53"
5. The vertical distance from the rim of the two slab sections to the lower part
of the boss = 6 inches.
6. The height of the boss = 5 inches
7. In the previous design of the boss (another post) base on this geometric
configuration I determined, all the boss dimensions including its 1inch
thickness, using only the 4 inches radius of the base.
Therefore, the references show that the granite leaf dimensions, and the boss
location is exactly as determined by my design. I have shown that the Phi point
corresponds to the location of boss in the slab. Nobody would think that
starting the design with a number, which is not part of the granite slab
dimensions, would give us all the granite slab dimensions. Therefore, we can
only think that the design method used by me was the same used by the Egyptian
designers. Besides, the geometrical configuration should be common in both
designs.
The fact that the boss was located at the Phi location of the design, is of most
importance. This is only possible to find and determine, by using my geometric
configuration. Therefore, the geometric configuration is like a "geometric key"
that opens for us, the geometry used by the ancient Egyptians to design the
Great Pyramid and all its chambers.
This also shows that this ancient engineers knew more about what we called
today, the "golden section", than we think. To me, this is the message received
from this poor, and irreverently carved object called "construction boss" by
many people.
This is very important! The fact that the location of the carved object was
placed exactly at the Phi point could only be found using the geometric
configuration. There is no way to find that the dimensions of the slab were
generated by a simple geometric configuration, and that this configuration is
the same I discovered many years ago for the Great Pyramid, and I presented here
for all to see. In other words, nobody will ever know that the boss was located
at the Phi point of the design granite slab, if it not were using my geometric
configuration.
This configuration for the Great Pyramid acts like a generic drawing, where no
matters the size of the object; we get a scale model of the pyramid's design, as
in this case, from the enormous size of the Great Pyramid structure, to the size
of the little boss.
As I stated before, I also discovered the configurations applicable to Kephren, Mycerinus, Red, and Bent Pyramids. They are
all different configurations,
different characteristics, but interlaced one to the other. Each design confirms
the existence of the other. This shows us that Pharaoh Sneferu, taught his son
Khufu how to configure the geometry to build Pyramids. The configurations used
by Sneferu for the Red and Bent Pyramid, and this one used by his son, show us
extra ordinaries characteristics in geometry, many of them not known or
visualized by researchers.
Is this just a miracle? Could it be a multiplication of coincidences? Do we need
more proof that the granite slab and its boss is more than a stone place there
with the purpose of releasing the portcullises, as Mr. André Pochan suggested in
his book? If the intentions were to place the slab to raise its upper section by
means of the boss in order to release the ropes, holding the portcullis system,
why they needed to level and uniformly cut 1 inch from the whole front of the
upper section and also from the lower section, to carve the boss? The slab
thickness was already set for the grooves, why carve all the front side? Do you
really think that the boss was carved with such exactitude, in such location, to
only be used to lift the slab?
If the boss were placed here as a coincidence, it will be the greatest
coincidence in the World. However, we know that the center of the boss was
(apparently) displaced 1 inch, to the west side, however, keeping the same
elevation, or the same proportion of Phi, in the design.
Let's take a look to the stone frame that encased the granite leaf. Let's refer
to the following figure:
Let's say that the designer, to emphasize the vertical distance from the top of
the small pyramid to the top of the boss, used this measurement as the
horizontal distance to encase the granite slab (24 inches). Therefore, he set 12
inches to each side of the front window of the slab, having a width of 40.54
inches. What happened? He obtained a total width for the system equivalent to
40.54 + 2 (12) = 64.6 inches! However, he had 65.6" available, that is, one inch
more. Therefore, the front window of the granite slab instead of 40.54" as
designed, has 41.6", equal to 65.6" less the 24" (from the 2 wainscots) = 41.6".
This is the actual window measurement of the slab.
So, 65.6" less 48" for the granite slab =17.6", divided into two sides = 8.8"
for each side, inside the wainscots. Since the wainscots are 12", the grooves
depth should be (12.00  8.8) = 3.2". This number agrees with the grooves depth
measurements.
Just thinking: I am still working on this. Is it possible that if the granite
slab could be move horizontally to the west side, inside the grooves, for 1
inch, the center line of the complete slab (and the boss) will move 1 inch to
the west side of the front window. Since the slab has its ends inside the
grooves it will not be noticed from the front window. This inside movement can
not be detected, except that the boss center will appear to be displaced 1 inch
to the west of the center of the slab. The center of the front window of the
slab will be maintained, therefore, the boss will appear as been displaced
1inch to the west of the slab's windows center, which will continue to be 41.6
inches width by 51.57 height.
See the following figure.
In accordance with my geometric
configuration, the boss would be located in the Phi position of the design. I
called it point X'. This point is 6 inches above the joint of the two sections;
you can see my previous drawings in that post. My prediction specified the boss
would exactly be located at 6 inches over the two granite junctions.
I scaled a front view photo of the boss and superimposed it over my design
drawing prediction of its location. I set the photo so that the junctions of the
two granite divisions hold an equivalent position in my design, and the photo.
It is interesting to observe that being the granite slab so large in space, the
location of the boss in your picture just exactly fit and confirm the elevation
position of the boss as I predicted, based only on the width of the antechamber.
You can also observe in this figure the predicted 12 inches wainscots spaces, as
you saw in the south antechamber's wall. If all of these are coincidences, I
think they are good ones.
Nevertheless, this displacement could have happened unintentional when lowering
the granite slab. If the slab was lowered and just by chance set close to the
west end of the grooves, the effect would be the same.
I continue my exploration in this field and have found:
For the nonbelievers, there is much more. The length of the entrance lower
corridor to the antechamber is 51.57 inches (exactly the same height of the
granite slab). The elevation of the east wainscot, measure vertically from the
antechamber's floor, was set as twice the granite leaf height = (51.57) (2) =
103.14!
What about the horizontal length (100.8 inches) of the second horizontal
corridor going into the King's Chamber? Project this distance vertically, from
the base of the floor and the south wall side, and you will get the exact
elevation of the three portcullis slabs, before been lowered. In other words,
the dimensions inside the antechamber seem to respond to a wellset geometry.
Were all these complex calculations done using the simple Egyptian arithmetic's,
shown in the Egyptians found papyrus?
To me, it is something incredible to think that such massive stone blocks, as
those at the south wall of the Grand Gallery, were cut at the same length as the
granite slab height, just as a coincidence!
If the boss was any rough carving to lift the upper block, why was it placed in
this particular location corresponding to Phi proportion? Why the boss design is
the same design used for the granite slab? Why the same design corresponds to
the Great Pyramid? If this boss is as Petrie and his followers stated " is
merely a very rough projection, like innumerable others that may be seen; left
originally for the purpose of lifting blocks", why it has all characteristic in
consonance with the slab and the antechamber dimensions?
As the boss is labeled of no interest, or value, the same happens with my
Perfect Symbol. It characteristics are unique, much of them unknown.
Therefore, there is a reason for the ancient Egyptian Pharaoh and his engineers,
if they knew about this, to use the same for the construction of the greatest
Pyramid ever build.
Are these the greatest coincidences of the World, or as I stated, the
engineering knowledge attached to the ancient Egyptians is far more than the
very simple methods we pretend to apply to them as corresponding with the
supposed technology of that time and age.
References:
1. The Great Pyramid, Piazzi Smyth: Pages 200212
2. The Pyramids and Temples of Gizeh, W. M. Flinders Petri with and update by
Zahi Hawass. Pages (2527)
3. The Egyptian Pyramids, J. P. Lepre, Pages 8692
4. The Mysteries of the Great Pyramid, A. Pochan, pages 3135
5. Egyptian Pyramid Geometry, Hadyn R. Butler, 1998
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