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:


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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.



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I used the Perfect Symbol to explain the geometry involved in the design of the Great Pyramid.

  1. to explain the geometry involved in the antechamber design.
  2. to explain the geometry involved in the pyramids of Chephren, Mycerinus, Bent, Read, and many others.
  3. to explain the geometry involved in Leonardo da Vinci's drawing for the human body proportions.
  4. to explain the Pyramid's layout Plan in Giza.
  5. to explain the reasons and construction of the boss.
  6. to explain the Pyramid's ventilation shafts design.
  7. to explain many important architectural drawings of buildings.
  8. 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 re-located 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.



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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 set-up 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.
 


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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.
 


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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.



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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.
 


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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 1-inch 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.



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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 1-inch 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.



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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.

N
evertheless, 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 non-believers, 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 well-set 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 200-212

2. The Pyramids and Temples of Gizeh, W. M. Flinders Petri with and update by Zahi Hawass. Pages (25-27)

3. The Egyptian Pyramids, J. P. Lepre, Pages 86-92

4. The Mysteries of the Great Pyramid, A. Pochan, pages 31-35

5. Egyptian Pyramid Geometry,  Hadyn R. Butler, 1998

 



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