The Mathematics of the Great Pyramid


The Descending Passage                                                                                            

The Descending Passage, “the Descent” is 4147.30909 inches from the pyramid entrance to its termination at the entrance to the Subterranean Passage. It has a vertical drop of 1852.967118 inches. The entrances to the two passages that lead to the upper chambers, one near the top and one near the bottom, originate on the West side of the Descending Passage.

The first one, the Ascending Passage, has its entrance in the roof of the Descending Passage. Its virtual beginning, the extended floor line to the Descending Passage floor, is 1110.046329 inches from the pyramid entrance. There are three massive impenetrable granite stones blocking entry so that it  cannot be navigated, and which will be addressed in the chapter on the Ascending Passage.

The entrance to the second upward passage, the Well Shaft, has a square opening that is parallel to the base so that its lower northern corner touches the Descending Passage floor, while the bottom southern corner is 15.8113883 inches, the square root of 250, and vertically above the Descending Passage floor. This is the only way up, excluding the modern passage skirting the granite blocks in the Ascending Passage, and is a rough torturous climb.

The first significant number encountered is the 481.1252243, the number of inches from the pyramid entrance to the scored lines on the walls on both sides of the Descending Passage. This is the foot equivalent of the pyramid’s height but as inches, it should be considered a twelfth of the height, because besides being the pyramid’s radius-height and the ratio between Sixth line and Third line it is also a twelfth of the earth’s ideal yearly circuit around the sun, a month.

  Confirming that it should be taken that way is the product of multiplying it by the second measurable aspect, the scored   lines to the virtual beginning of the Ascending Passage on the Descending Passage floor. This distance is 628.9211044 inches, and as a number is 2 pi (First line divided by Sixth line) in the second golden proportion related pi of 3.144605522, this one generated by using the golden proportion to square the circle. This same number appears at the bottom of the Descending Passage as well. The product of multiplying the two numbers together is 302589.8064, one twelfth,(times 100) of 36310.77677, its Third Line’s ratio to First Line,(the circle). Half of this Action ratio is 1815.538839, the length of the Grand Gallery. So right off, two twelfths occur; the first a twelfth of the Earth’s ideal distance around the Sun and the second, a twelfth of Third Line’s Action principle enabling the movement through space. The first number representing Space and the second one representing Time.     

The next significant number is the distance from the virtual beginning of the Ascending Passage on the floor of Descending Passage, down the same distance as the Ascending Passage length of 1546.550789 inches. This leaves 1490.711985 inches ( square root of 22222.22222, as well as a third of 4472.1359) to the bottom of the passage. This number is important not only because it appears in the Subterranean Passage but also because it is a quarter of the sum of the two angled passages that can be traversed, the Descending Passage and the Grand Gallery. This sum of 5962.847939 inches,(square root of 355555555.55) divided by 1000 is a 48th of the 286.2167011 inch displacement of the entrance from the pyramid’s East-West center. 1490.711985 divided by 100 is a 19.2th of 286.2167011 as well as being a quarter of 59.62847030 and is used often in the Pyramid.

Starting from the entrance, there are four separate routes that measure 4472.1359 inches, 1000 times the ratio for First Line divided by Fourth Line in the perfect world of the Square root of 10. This ratio represents the transition from the second dimension into the third dimension.

The first three of these terminate at recognizable points in the passage system. The first one runs from the pyramid entrance down the Descending Passage to the Ascending Passage, up the Ascending Passage and then through the Grand Gallery to the base of the Great Step. The second one follows the same route but instead of going up the Grand Gallery it veers off to the Queen’s Chamber and terminates in the Niche. The third one goes down the descending Passage and through the Subterranean Chamber Passage to a point just past the North-South center line within a space containing  measurements of 44.721359 and 4.4721359, two 14.90711985’s and one 59.6284794. The fourth one and the only one that one can actually take upwards, goes down the Descending Passage to the Well Shaft entrance and then up it to a nondescript point in the shaft. The fact that it ends in the shaft is what is important, a foot in the doorway, so to speak.

The Well Shaft entrance is a tour de force of the square root of 10 and will be gone into later, but there are some important measurements from its entrance to the bottom of the Descending Passage.           

The first one is the distance between the Well Shaft entrance’s north side and the bottom of the passage, 295.877104 inches. When Added to the 350.72167 inches from the passage bottom to the Subterranean Chamber the sum is 646.598774, whose inverse is .001546554123, the Ascending Passage being 1546.550789 inches, a difference of 3 thousandth of an inch.

Secondly, from the center of the opening, dropped vertically to the floor of the Descending Passage, to the passage bottom is 278.1994344 inches. The sum, when added to the 350.72167 inch distance from the beginning of the Subterranean Passage to the Subterranean Chamber, is 628.9211044 inches, the same Golden Proportion generated 2 pi occupying the space between the Descending Passage’s first 481.1252243 inches and the Ascending Passage. So the top and bottom of the passage reflect the same pi. 

The third important measurement is from the Shaft opening’s south edge dropped vertically to the floor of the passage, to the bottom of the passage which measures 260.5217649 inches. Squared, it is 67871.59471 inches, 10 times one side of the pentagon in the Pyramid’s circle, the symbol for  human.

The angle of the Descending Passage from the entrance to the Ascending Passage is 26 degrees, 30 minutes and 48.79 seconds, and from the Ascending Passage down to the passage bottom is 26 degrees 32 minutes and 47.88 seconds. These angles are different from Petrie’s because of errors of the length of the passage due to the difficulty of measuring over the debris still in place when he measured and the fact that besides the casing stones being missing, many of the core stones at the entrance are also not there. How ever, the mean of 26 degrees 31 minutes,48.34 seconds is but 25.52 seconds greater than Petrie’s mean. All angles stated here are developed from the right angle triangles created by the passage system in the second dimension plan and not from the three dimensions of the pyramid as built.

Of all the measurements within the pyramid, the most difficult to nail down are the heights and widths of the passages. One would think these would be the easiest because of the many measurements taken all along the passages by all the various measurers. It would seem to be the one place where a mean would be applicable. The Descending Passage width averages of both Flinders Petrie and Professor Piazzi Smyth are the same, 41.53 inches.  Mathematician and astronomer John Greaves, who measured the Great Pyramid in 1638, had a mean of 41.56.  From a number’s point of view 41.56921938, a purification of Greaves number is a better fit as its half measure, 20.78460969 is used elsewhere and its connection to the twelfth part of the pyramid’s height, being its inverse. Another possibility is 41.61791451 which is the square root of 1732.050808. 41.20226592,twice the Golden Cubit or two thirds of the Golden Proportion, is used as the width of both the Grand Gallery and King’s Chamber passage.

The perpendicular height is probably 47.28708045 instead of the consensus of 47.24-26, because of its connection to 5, being the square root of 2236.06797. Another good prospect is 47.12461196, which is the height of each of the 5 courses that make up the walls of the King’s Chamber. One hundredth of the Descending Passage’s length, 41.4730909 is another possibility. One would think the area or volume of the Descending Passage would decide the issue, but no such luck. 

There are some other numbers that can be developed within the Descending Passage that should be mentioned because they are close to important numbers even though they are not the specific number. Often the difference between what it is, and what it looks like it should be, is the important number, though not the case in the Descending Passage.

Two measurements deal with 286.2167011, the east-west displacement number. The first one has to with the distance from the center of the Well Shaft entrance, dropped vertically to the floor of the Descending Passage. This 7.90569415 inches (the square root of 62.5), a fourth of the square root of 10, and, times 1000, is the ideal diameter of the Earth. When added to the 278.1994344 inches from the passage bottom up to the center of Well Shaft opening on the passage floor, the sum is 286.1050786 inches, a .1116325 inch difference.

Then, if the 7.071067812 inch measure of the perpendicular from the passage floor to the center of the bottom of the Well Shaft opening, is added to the sum of the opening’s perimeter, diagonals and the vertical and horizontal side bisectors, the total sum is 286.2503858, .03368 greater than 286.2167011.

From the Ascending Passage’s virtual beginning on the Descending Passage floor down to the same point on the Descending Passage floor marked by the 7.071067812 perpendicular, is 2755.52779 inches. The inverse of 2755.535376, (a difference of .00758), is .0003629056834, which when multiplied by 100000000, is 4 times the pyramid’s south base line. 3.629056834 is Third Line to First Line in the world of 7, whose pi is 3.142857,(22 divided by 7).  

There are also two separate 278 inch measurements, whose mean of 278.238735, is .067 from being the 4th root of 6000000000. The individual measurements are 278.1994344 inches, bottom of passage to center line of the Well Shaft opening vertically dropped to the passage floor, and 2782.780356 inches, the distance from the center of the Well Shaft opening down the vertical to the passage floor, 23.71708245 inches (square root of 562.5) and then up to the entrance of the Ascending Passage’s virtual beginning on the Descending Passage floor.  

The symbolism of the Descending Passage clearly has to start with the universal association of down with negative and up with positive. One enters and can only go downward, leaving the light of the natural world behind. It must always be kept in mind that the route taken inward must be reversed in order to leave the pyramid and regain the light. And since the first measurable section of the passage system (entrance to Scored Lines)is the foot measurement of the pyramid’s height and radius of pyramid’s circle, in inches, emphasizing Sixth Line’s role of knowing that the created and the creator are one and the same, reiterates this principle because it is also the last section to pass through when exiting the pyramid.

Then, when the first section is multiplied by the second section (scored lines to Ascending Passage) which is the ratio between Sixth Line and First line in the golden proportioned world, the product is a twelfth of that system’s Third Line’s ratio with First Line, as well as being the ideal distance the Earth travels around the sun in a month. The same Sixth Line to First Line ratio is coupled at the bottom of the passage with the pyramid’s symbol for human, 6.787159471, one side of the pyramid circle’s pentagon and the ratio between Fifth Line and Third Line. Part of the ratio is in the Subterranean Passage, numerically pulling one across the threshold of the Subterranean Passage.   

Although the entrances to the upward passages that begin in the Descending Passage will be discussed later in full, the following may be surmised at this point. The Ascending Passage with its direct route of 4472.1359 inches (Fourth Line ratio to First Line in the square root of 10 world times 1000) was the designed route up to transformation into the third dimension, Fourth Line’s job. Adding to this assumption is the fact that the virtual beginning of the Ascending Passage is 173.2050808 inches (100 times the symbol for the third dimension of volume, the square root of 3) above the pyramid’s base This is the theoretical path for all forms of life, all forms except us.

The Well Shaft of Life, as it is called, measures 2236.06797 inches in length, which, divided by a thousand is the actual measurement of Fourth Line in a circle of one in the square root of 10 world from which the ratio is derived. It is the Designer’s decision that the way up for humans is the school of hard knocks, that experiencing the actual, rather than the principle, is a necessary step for humans, whose free will through cognitive choice separates us from all other forms of life, as we humans deal with right and wrong, could and should every moment of our lives.

Using the Ascending Passage is not a choice left to humans. The only way up is to first go down the Descending Passage to the Well Shaft, and then up the steep, rough and narrow 2236.06797 inches, a perfect illustration of having to pull yourself up by your own boot straps. No one can do it for you, just as every one has to live and experience their own unique life.

Free will, which is an educated guess as to what it is that has to be learned-experienced by the rough road of the Well Shaft of Life, does however, come into play at the shaft opening. Although the perfectly square entrance is sharply cut, the actual passage is cramped, rough dangerous and not appealing in any way, where as the smooth walls, ceiling and floor of the Descending Passage make it comparative spacious and safe. That’s the choice for free will at this point in the pyramid.

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