The Mathematics of the Great Pyramid


                                                                                 The Great Pyramid’s exterior

     The height of the Great Pyramid is to its base perimeter as a radius is to a circle’s circumference, the base being a square version of a circle. Although the Great Pyramid is not the product of a particular circle-squaring operation because the four sides are not equal, it never the less should be considered, in principal at least, to be the product-child of the union of its mother, the circle, representing the spirit side of All, and its father, the square, representing matter. 

     The radius-height is the geometer’s thought being manifested into reality through the action principle of Third line. In the Great Pyramid, the particular dimensions of the radius-height and circle-square express that principle through number, as the measurements of both are Third line ratios, Third Line to First Line and Third line to Sixth line. Both are generated by the number 3 and are connected to it in many different ways.                                          

     The first way deals with the height of the pyramid. In the case of Great Pyramid, the original height is unknown because there is nothing left of the apex and only a few of the casing stones remain that formed the exterior. Even though the corner stones no longer exist, the four corner points of the base have been determined so that each side of the base could be measured. The few remaining casing stones have not revealed a definitive angle with which a height can be computed. The slight differences between the various angle measurements of the different researchers produce extreme differences when projected up the pyramid’s slope of some seven thousand plus inches, so that all stated measurements for the height are simply educated guesses based on what the particular researcher accepts as the angle of the pyramid’s slope, determined by the casing stone angle. These heights range roughly from 480 to 485 feet. Petrie’s estimation of the height is 481.133 feet, which is 5773.596 inches.

      However, in spite of this quagmire of hypothetical heights, and perfectly illustrating the process used to refine and define all other numbers in the pyramid, one obvious choice emerges from the pack, as it is number royalty. This number, in feet, is 481.1252243. But more important than it’s measure in feet is it’s measure in inches, 5773.502692, 10,000 times the inverse of the square root of 3 (1.73205), geometry’s representative of the third dimension. This is only .094 less than Petrie’s estimation. When divided by 10,000 to it’s essence of .577350269, it is the ratio between Third line and Sixth line,(Third line times .57735 equals Sixth line) or Sixth line times the square root of 3 equals Third line. Besides being the inverse of the square root of 3, it is also a third of the square root of 3 and the square root of .333333333.

      With very few exceptions, the position of the decimal point is irrelevant, as it is the sequence of digits comprising the number and its function as a ratio that counts.

      And, since 577350269.2 miles is the distance the earth travels around the sun in the idealized time and space plan of the Earth, Moon, and Sun, 48112522.43 miles is one twelfth, or a month, of our yearly passage through space. 

      In addition to this, the very first section of the descending passage up to the scored lines is 481.125 inches, so that entering and exiting the pyramid, one traverses the inch version of the height in feet, symbolizing “as above so below” and Sixth line’s principle of recognizing that the created is identical to the creator.

      But more importantly, when Third line is created halfway in the process of one circle becoming two circles and whose measure is taken to be one, the height of the Great Pyramid is 10,000 times the space between the centers of the two overlapping circles which are no longer one but not yet two. They share a common Third line and the Great Pyramid is their common radius and is what is between One and Two.

      The second way 3 is involved in the exterior of the Great Pyramid is the why of that height. The architect’s rational for choosing this ratio for the pyramid’s height is its unique influence on the rest of the pyramid and the circle it defines with it’s height, as it performs a function that no other number can. 

      What it does in the circle of the Great Pyramid is to make the measure of Third line,(one side of the equilateral triangle) an even 10000 inches(5773 x 1.73205). Reduced to it’s most refined essence, Third Line can be taken as One, placing emphasis on it’s principle of action.

     Then, because the quotient of any number divided by one is the same as the number being divided, the ratio between Third line and all other lines of the pyramid and its circle, IS the same number as the particular line’s actual measurement. This is the radius voicing its thought, stating that this is what the pyramid is all about, Action’s relationship to every thing else.

     Therefore, whatever the Great Pyramid’s base perimeter measures, which is taken to be theoretically identical to the pyramid’s circle, IS the ratio between Third Line and First line, divided by 10000. So the Great Pyramid, the 5 sided child of the marriage between circle and square, has a height-radius that makes Third line a surrogate ambassador for 1, as idea can’t manifest into the thoughts form without the function of 3’s action principle. And not only does everything in the universe of All happen through 3’s principle of action, but  every line in the pyramid also honors this principle resulting from its height’s ratio making Third line 10000 inches or One. 

      The third involvement with the number 3 is with the actual measurement of the base perimeter. Petrie’s and Cole’s perimeter measurements of the Great Pyramid’s base are extremely close in spite of the 36 thousand plus inches being measured. But Cole’s 1921 survey for the Egyptian government is the standard. And in spite of the best equipment and a cleared base, each side’s measurement is accompanied by a plus and minus margin of error.

      Cole’s total base measurement is 36277.836 inches while Petrie’s is 36277.824 inches, only .012 difference, a minor miracle in pyramid measurements. It has long been thought that the perimeter reflects a half minute of equatorial latitude. Now a half minute of equatorial latitude is 36277.824 according to the U.S Dept. of Commerce’s National Institute of Standards and Technology, which matches Petrie’s figure.                                      

      This would seem to be conclusive except for the fact that there is no definitive set of absolute measurements for the Earth because it is an ever changing irregular spheroid, so that a degree of latitude is simply a 360th of an agreed upon measurement of an impossible to measure spheroid. There have been a number of attempts to measure the Earth’s spheroid including all the irregularities and anomalies, each being slightly different than the last, so that a half minute of equatorial latitude would be 36275.354 inches according to the Clark spheroid, 36277.25056 according to Helmert’s spheroid, and 36278.07077 according to the International Spheroid.

      There is, however, like the geometric measurement of the  pyramid’s height, a number that fits this approximation and is at the same time connected to the height-radius of the pyramid’s circle and it’s triangle. That number is 36277.73439.

      This is taken to be the pyramid’s perimeter length because of its genetic ties, it being the eighth root of 3 to the thirty sixth power. This number is less than Petrie’s 36277.836 inches by .09 inch and Cole’s 36277.25056 by .102 inch. The Great Pyramid’s architect uses 36277.73439 inches because of it’s lineage to pure number, the third one at that, making the point that there is order to All, even to the orderly division of our planet, and that Number itself is that order. Not only is man the measure of all things but so is our planet.

    Then, because the length of the base perimeter is theoretically the same measure as the circle’s circumference, making the measure of the base perimeter the same number as the ratio of Third Line to First Line; 36277.73434 inches (the perimeter measure of the Great Pyramid’s base)/ 10,000 = 3.627773434, so that by moving the decimal four places, the perimeter IS the ratio for Third to First Line, the Action ratio in a world according to 3.

      It can be read symbolically as the relationship between Time and Action and can also be generated by multiplying the eighth root of 3, times the square root of 10, times 10 to the  fourth power, or multiplying the eighth root of 1875 times the square root of 2 and then multiplying by 10,000.            

      Then, because the Great Pyramid’s base is not square but is technically a quadrilateral, as each side is different, each side could be considered one side ,or a fourth , of a true but imaginary square, making for four separate perimeter lengths with four additional third line to circle ratios. The same could be done with the east-west meridian and the north-south meridian. These different versions of the same ratio could be looked at as different points of view, each a world of its own. This is the purpose of the pyramid’s base not being square.  The south side is the longest and is 7.27 inches longer than the shortest side which is the north side. The east and west sides are just 1.45 inches different.

      Although these Third line ratios are not familiar to anyone as numbers because they are not in use, the Second Line to First Line ratio, (pi), IS a number that is universally recognized and used. Up until Newton’s calculus proved that 3.1415926 is pi, many different numbers were used at different times and places throughout history. The Great Pyramid’s exterior is a tour de force of these numbers, each side expressing a specific pi number, determined by multiplying a side by 4 and then dividing it by twice the height of the pyramid, Second Line, which is the diameter of the pyramid’s circle and is also the ratio between Second line and Third line. This arrangement can be considered an opportunity to view the world through different colored lens. 

      Two sides, the west and south, were obvious. The west is 9069.135 inches, only .05 less than Cole’s figure, and .13 less than Petrie and generates 3.627654330 as Third Line to First Line ratio and 3.14164078 for Second Line to First Line ratio. This pi number, one of the two pi’s relating to the golden proportion, is a manufactured number and can be generated by a number of methods, the most familiar being the product of the golden proportion squared, times 1.2 and the simplest being the square of 18 plus 1.8.  The other pi relating to the golden proportion is 3.144605512, which is developed by using the golden proportion to square the circle. It is the second easiest circle squaring solution and it’s Third Line to First Line ratio divided by 2 (1815.538839) is the floor length of the pyramid’s Grand Gallery. Both numbers are involved in the passages and chambers within the pyramid.

      The south side measures 9072.647086 inches and is .36 less than Cole’s figure and .21 less than Petrie’s. Its Third Line to First Line is 3.629058834 and its Second Line to First Line ratio is 3.142857142, created by dividing 22 by 7, is still in use today by engineers in the field, due to the simplicity of its fraction.

      The east side measures 9070.60498 inches, .07498 greater than Cole.  Its Third Line to First Line is 3.628241992 and its Second line to First Line is 3.142149737. This side’s numbers appear to have no intrinsic value as a number or ratio, is found no where else in the pyramid, and must be considered a filler in order to arrive at the desired total perimeter measurement.

      The north side is 9065.346554 inches, .246554 greater than Cole’s figure. Its Third Line to First Line ratio is 3.626138621 and its Second Line to First Line ratio is 3.140328164. This is a very low number for pi yet it turns up with a prominent role in the Anti-Chamber with an important connection to the King’s Chamber which no other pi number can accomplish. But its more dramatic importance is its relationship to the south side.

      When added to the south side and then divided by two in order to arrive at the east-west meridian’s dimension of 9068.99682 inches, its Third Line to First Line ratio is 3.627598720 and its startling Second Line to First Line Ratio is 3.141592654, actual pi, arrived at many thousands of years ago.

      Four other Third line to First Line ratios can be developed by using the corner socket lines. The corner sockets are under the corners of the pyramid but also extend outside on the pavement. They are very irregular in shape, much eroded, and took a great effort just to find and then locate the outside points. Their purpose is thought to have to do with marking the diagonals of the pyramid. The only recognizable number is the line running between the two north side sockets measuring 9128.709292 inches. This is a fourth of 36514.83717, whose Second Line to First line ratio is the square root of 10,(3.16227766) the only circle-squaring solution demonstrating equality of curved line and straight line, the two representatives of Spirit and Matter. Both metaphysically and literally, this invisible line must be crossed in order to ascend and enter the pyramid, and is the principle overall number system in the Great Pyramid.

      So instead of using one set of ratios, the Great Pyramid’s exterior presents multiple versions of ratios for the same line, each with its own point of view as to the nature of reality. The two golden proportion pi represent Fifth Line, 22 divided by 7 brings its repeating six digits into play, and so on , each representing its own world. Of all of them, the square root of ten produces the purest numbers for its ratios to First line, the circle, such as the square root of 13.3333333 for Third line to First line, the square root of 20 for the Fourth Line to First line and the square root of 40 for its Sixth Line to First line.

      The fourth way that 3 involves itself in the Great Pyramid is the ratio of Sixth Line (height-radius) to First Line (circle-square). The 2 pi ratio of 6.283487916 it develops with the full perimeter measure of 36277.73439 inches, can be achieved by multiplying half of it by the square root of 3, or the 8th root of 2430000. Its pi is 3.141743958.

      The fifth way 3 is involved with the Great Pyramid is with the standard ratio between the Second Line and Third Line which is 1.154700538, (the square root of 4 divided by the square root of 3, or the square root of 1.333333333). Second Line (the diameter), being twice Sixth Line ( height-radius), is 11547.00538 inches.  In the ideal plan of the space-time relationships between the Earth, Sun and Moon, its inverse, 866025403,(square root of 75, or the square root of 3 divided by 2) is the diameter of the sun in miles. When squaring the circle according to the square root of 10, using its Third Line ratio to First Line(circle-Square) of 36514.83716 as the base perimeter and the Great Pyramid’s height, 8660.25403 would be the measure of each of the pyramids four vertices. These are traceable to the altitude of the circles triangle, becoming one half of the pyramids eight primary exterior lines, the other four being the four lines of the base square, making 4 from the circle and 4 from the square…….equality. The Great Pyramid’s vertices don’t measure this because the base perimeter is not 36514.83716 inches. However, the altitude of the pyramid’s circle triangle does measure 8660.25403 inches.

      In the great Pyramid, 8660.15403 inches is the distance from the entrance to the East-West center of the pyramid in the King’s Chamber via the only way up, the Well Shaft, which was not an after-thought but a major part of the original plan. So its relationship to the sun, its role in the union of spirit and matter, circle and square, curved and straight, and it being half of the in and out journey in the pyramid, as well as being half of the square root of 3, the symbolic representative of the third dimension, makes it an important number in the Great Pyramid.                                                              

      The sixth way 3 is involved in the exterior is the pi ratio between Second Line and First Line. This ratio for the 36277.73439 inch base perimeter is 3.141743958 and can be developed by dividing the base perimeter by 2 and multiplying it by the square root of 3.

      An interesting consequence of the height of the pyramid being 5773.502692 inches, is that there is an equation, unique to the Great Pyramid’s height, for developing pi for every possible square base. When a pyramid’s height is 5773.502692 or any power of it, and no other height, the square root of the sum of both the base’s diagonals squared and the sum of the cross whose lines bisect the four sides of the base’s sides, squared, equals pi for that particular square-circle.                 

    It does this because the result of this equation is the same as dividing the square by 1.154705. It becomes a pi number when the square in question is the base of a three dimensional pyramid with the Great Pyramid height of 5773.50269 inches, because 11547.05 is the diameter of its circle. 

      In the Great Pyramid it reinforces treating each base side as the seed of a square in its own right, besides being a fourth of the pyramids base perimeter, and treating a square as if it were a circle.

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