The Mathematics of the Great Pyramid


The Crossing of the Pure Roads of Light

The junction of the Well of Life, the Ascending Passage, the Grand Gallery, and the Queen’s Chamber Passage is called the crossing of the pure roads of life in the Book of the Dead. But because of the quantity of numbers involved in this junction and the influence they have on the rest of the upper chambers and passages it could easily be called, from numbers point of view, Grand Central Station, crossroads of the world.

 A general description of this junction is that the Ascending Passage continues into the Grand Gallery a few feet and then drops down a half a foot to become a horizontal passage that runs south directly under the Grand Gallery to the Queen’s Chamber. The Grand Gallery passage floor continues after a distance of about 22 feet. Just before the continuation, a drop of 9 inches occurs that is known as the second cutoff. This continues 40 inches downward and northward, parallel with the passage to the first cutoff, which allows for the entrance to the Queen’s Chamber passage. This 9 inch section is for a theoretical bridge crossing the gap in the Gallery passage floor. There are 5 slots on each side that are thought to be supports for the bridge. This bridge would be about 20 feet long. There are ramps on each side of the Gallery passage that begin at the north wall of the Gallery. It is through a gap in the west wall that the Well Shaft enters the Gallery.There are many dimensions to be addressed here but they can’t be unraveled or understood without dealing with much of the rest of the Pyramid, because each of the dimensions is determined by,  interconnected with, and dependent on other aspects of the upper chambers and passages, the most important of these being the various elevations

The elevation of the beginning and end of the Ascending Passage has already been established as 173.2050808 and 678.7159471 inches respectively, making the junction with the Grand Gallery 851.9210279 inches above the pyramid’s base. The elevation of the base of the Great Step where the Grand Gallery passage terminates is determined by the lengths of the Grand Gallery passage and the Queen’s Chamber Passage, the two parts of a right triangle. These two dimensions, as well as that of the Ascending Passage and a few others that come into play, are identical to Petrie’s steel tape measurements but with the rest of the digits beyond the tenth of an inch that he gives. This is another illustration of the validity of the process of determining measurements by the quality of the number.

The Grand Gallery passage’s length is 1815.538839 inches, which is half (times 1000} of 3.631077677, the Third Line to First Line ratio in the Golden Proportion ruled world, Petrie’s measurement being 1815.5 inches. The roof ridge running east and west in the Queen’s Chamber is directly below the face of the Great Step, both marking the north-south axis of the pyramid. The Queen’s Chamber passage from the north wall of the Grand Gallery to the north-south center of the chamber, which is directly below the vertical face of the Great Step, is 1626.576562 inches, the square root of the square root of 7 to the 12th power,(1626.5 by Petrie). The Ascending passage is 1546.550789 inches, 1546.5 inches by Petrie.

By Pythagoras then, the vertical distance between the Grand Gallery and Ascending Passage junction up to the base of the Great Step is 806.492383 inches and from the pyramid base, 1658.413411 inches.

Although the Great Step has some major intentional irregularities with multiple measurements which will be addressed later, the principal face height is 35.35533906 inches, the square root of 1250, making the floor of the King’s Chamber passage 1693.76875 inches above the pyramid’s base. The measurement from step face (center of North-South axis) to the south wall of the Grand Gallery is 61.8033988 inches, the golden proportion.

Another important factor in determining various elevations is the height of the first low part of the King’s Chamber passage, which starts at the south wall of the Grand Gallery. This is 43.70160247 inches, the square root of 1909.83005, 1.90983005 being the ratio between the volume of cube and the volume of its inscribed sphere. 43.7 inches is the measurement given by of a number of Measurers. Its relevance is that when subtracted from 1732.050808 inches (always an important number no matter where it appears), which is 5.41954429 inches below the ceiling of the low passage when measured from the pyramid base, the result is 1688.349205 inches, very close to the 1688.37996 inches horizontal length of the Grand Gallery (the sum of the Queen’s Chamber passage plus the north south dimension of the Great Step’s platform).

There are a number of interesting vertical numbers that can be developed but none that equals the horizontal, which would make a square of height and length. The virtual extension of the sloping plane of the Grand Gallery floor passes through the Great Step, and intersects with the vertical plane of the Grand Gallery’s south wall 4.711856581 inches below the top surface of the Great Step, making the elevation of the intersection 1689.0506893 inches above the base of the pyramid. The foundation of walls of the King’s Chamber is 5.285390541 below its floor level making it 1688.473359 inches above the pyramid’s base. It is possible the depth of the slot in the Great Step is intended to be 5.388789 inches, making the vertical height 1688.379961 inches, but it is too ill defined to get a realistic measurement.

Another number that has to be taken into consideration is Petrie’s measurement from the footing of the Queen’s Chamber walls, slightly different from the rough sub floor, up to a joint level that runs around the chamber and marks the top of the entrance and the top of the mouths of the so called air channels on the north and south walls. This is 67.44 inches, the mean of many measurements taken around the chamber.  

From here on it gets very complicated due to a number of reasons. One is that, as mentioned in the Ascending Passage section, the passage floor continues into the Grand Gallery, making the Queen’s Chamber passage higher than the junction of the Grand Gallery and Ascending Passage. At the end of this extension is a triangular wedge that functions as the stopper for a theoretical bridge spanning the empty space between the end of the extension, and the resumption of the Grand Gallery passage. There are no reliable measurements for any aspect of the extension, partly due to the fact that almost none of it remains. The total of this extension, including the wedge, is 24.2939847 inches on the Grand Gallery’s passage angle. The Ascending Passage angle (26 degrees 1 minute and 51.48 seconds or 26.03102987) and Grand Gallery passage angle ( 26 degrees 22 minutes and 23.61 seconds, 26.37322418)  are slightly different but that difference is important.

Then, 1307.004294 inches down the passage to the Queen’s Chamber there is a downward step, of, according to Petrie, “about” a standard cubit. The range of other researchers measurements go from 19 to 24 inches. This discrepancy is partly due to the fact that the passage floor and the surface of the lower level, which continues on into the Queen’s Chamber, forming the sub floor for the missing floor, is very rough and not highly finished like the walls and ceiling. Petrie has no measurement for the passage height but others consistently make it around 46.5 inches.

It also must be mentioned that all measurers state the passage is not horizontal but drops up to two inches over the length of the passage. This is due to intention, subsidence, or error. Since the four corners of the pyramid’s courses at about the same level vary by tenths of inches and not inches, error seems unlikely. No rational for intention has surfaced, leaving subsidence as the likely cause. It is taken here to be at right angles with the vertical, because all the other measurements work out that way, and not when it is treated as an angle.      

There are more than 20 key vertical measurements connected the Crossroads to be resolved within the parameters of Petrie’s  measurements. Each one of these is extremely close to important numbers, but in most cases, using any one of them cancels out all the others. There is only one solution which allows for multiple important numbers, ten in all.

  So, 5.0366529 inches below the 851.9210279 level of the Ascending Passage junction with the Grand Gallery is half the  1693.76875 inch elevation of the King’s Chamber passage floor. This is 846.884375 inches and is what the level of the missing floor of the Queen’s Chamber should measure. The elevation of the footing of the chamber’s walls is 836.1243988 inches, which is 10.7599613 inches below 846.76875 inch elevation of the middle of the upper horizontal passage system. 10.7599613 is two times 5.3779988096 which is the Fifth Line to First Line ratio in the square root of 10 world. The reason for this is that it makes 173.2050808 inches the corrected height of the very important Niche in the Queen’s Chamber.

From this new floor up to the top of the door and air channels changes the 67.45078292 height to 56.69080672 inches. Neither of these numbers has importance in their own right but allows for two other important measurements. The first is the height of the air channels, which is 8.660254038 inches, the square root of 75 and a millionth of the idealized diameter of the sun. The measurement from the new floor level up to the middle of the air channel is 52.3606797 inches, the square root of 5 plus three, times 10, or 2.618033988 times 20. This vertical measurement is the same measurement as the horizontal measurement of the first low overhang of the King’s Chamber passage, which is almost directly above the air channels.    

 The sum of the two measurements below the level of the Ascending Passage and Grand Gallery junction is 15.7966289 inches. Adding 5.22182912 inches from above the junction level brings the Queen’s Chamber Passage elevation to 857.142857 inches, the inverse of 7 times 6000. So the total depth of the drop in the passage floor is 21.01345382 inches and with the addition of the bridge stopper’s height of 5.439776664 inches, it becomes 26.45823468 inches, the square root of 700.

In addition to these two uses of the square root of 7, there are two more, one horizontal and the other angled. These start at the north wall of the Grand Gallery. One is the virtual distance on the slope of the Grand Gallery’s passage, from the wall to the second cutoff, the hypotenuse of the Crossroads triangle. It spans the entrance of the divergence to the Queen’s Chamber and all the measurements below it and south of it that comprise the crossroad, the passage and the chamber. This measures 264.5823468 inches, ten times the depth of the distance one has to step down to the level of the Queen’s Chamber floor.

The second one is the distance from the Grand Gallery’s north wall, through the passage to the north-south center of the Queen’s Chamber, (its roof ridge) which is directly below the face of the Great Step. This measures 1626.576562 inches, the square root of the square root of 7 times 1000. All these aspects are in the domain of Seventh Line.

The journey to the Queen’s Chamber is controlled, structured and guided by the number 7, and all the symbolism it represents, as it determines the elevation of the passage, the length of the passage, the depth of the downward step, and the total distance of the divergence from ascending the Grand Gallery. All this in order to go to a 7 sided chamber containing a number of ratios that unite 7 with 5 and the Golden Proportion, and which contains an off center, three dimensional, five tiered, Golden Proportioned empty space in the chamber’s eastern wall that relates to, and is connected to, the King’s Chamber by ratios that come from the number 7.

There are 4 other key measurements relating to the bridge, the first being the length of the bridge itself. This measures 240.2811414 inches, which when squared is 57735.02691, ratio between Third Line and Sixth Line and, divided by 10 is the inch height of the pyramid. Multiplying length by the width of the passage, which is twice the Golden Cubit, 41.20226592 inches, and  by the thickness of 8.06860013 inches, and then subtracting the volumes of the triangles at the top and the bottom that would have to be removed to fit the space, transforming the six sides of the bridge slab into seven sides, the volume of the bridge is 79049.51302 cubic inches. Although this is 7.428484 cubic inches less than 79056.9415, the ideal diameter of the Earth, it could be taken as that because of its proximity to four other measurements.    

The first one is the distance from the Ascending Passage and the Grand Gallery junction up the virtual passage floor line to the first cutoff. This measures 223.606797 inches, the measure of Fourth Line in circle of one, and a tenth of the Well Shaft that one has just ascended to get to the point of encountering the next version of Fourth Line. Had the height of the Queen’s Chamber Passage been .01643635 less than it computes, it would have been the square root of the straight line measurement of the Well Shaft, 2154.434691, the cube root of 10.

Next is the height of what remains of the first cutoff below the 9.00594422 inches vertical height of the bridge. This measures 38.66973983 inches, the square root of the square root of 2236067.97.

The third one is the total passage length to get to the Crossroad’s junction from the pyramid entrance. This measures 6087.499951 inches, one sixth of the earth’s yearly revolution around the sun.

The last one is not a measurement but a number. That number is 5. There are five slots in the east and west walls that would accommodate the five supports for the bridge. The dimensions may have significance but the crudeness of the slots, which are not entirely vertical, make deciphering difficult. The significance is that there are five supports, which mimics the five changes of angle in the 2236.06797 inch long Well Shaft, as does the 223.606797 distance from the North wall of the Grand Gallery up the line of the missing floor to the first cutoff. It is hard to comprehend how the builders could carve sharp corners and smooth sides in the air channels that begin in the Queen’s and Kings chambers and proceed flawlessly at an angle through hundreds of stones over the distance of thousands of inches and  crudely carve the five sets of holes for the bridge supports. Unless it is purposely done for symbolic reasons. This contrast also occurs in the Anti Chamber.

There are a number of triangles that occur in the crossroads, a major one being the right angle triangle that has 223.606797 as its hypotenuse. If the height was 100 inches and the length of 200 inches, it would have the angle of 26 degrees, 33 minutes and 54.18 seconds, as the square root of 5 is the diagonal of two squares with a side of one. But it is not and is instead 26 degrees 22 minutes and 23.61 seconds, the angle of the Grand Gallery floor. In addition to this the length of the East and West wall sides have different dimensions which would change the other two sides. Something is not square and it probably is the cut off. It seems unlikely that the intersection between two passages would be off by over an inch in each direction.

The reason why this a factor is that there is an intentional deviation from square at the top of the Grand Gallery which allows for important variations in certain measurements, and having additional deviation at the bottom would be superfluous.
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