The
Great Pyramid Reveals a New Idea
Getting Back to Basics
The builders of a structure as magnificent as the Great Pyramid relied on teamwork as one of the essential ingredient for such a lofty endeavor. If mankind is ever to decipher any coded message that may be in this splendid structure will take the same spirit of teamwork from modern mankind to uncover it.
Returning to the basics allows the Giza Complex to establish parameters to express the concepts, principles and element that governed it’s construction and establish exact mathematical values for all the Pyramids different units of measure (cubits) and the formulas for derivation of each unit. Doing this has revealed a geometric construction used by the ancients making it possible to construct the Great Pyramid by squaring the circle as they did. The Giza Plateau and Great Pyramid provides a method for deriving the basic units of measure used in the construction of the Giza Complex those being the British Foot and inch. In order to accomplish this it is necessary to adhere to a one basic rule that rule is Assume Nothing. That means entering the complex with no preconceived ideas. Examine each item and let it reveal whatever information might be there. This is how I conducted the research and what the follows are the results of the study.
1. The use
of Fractions
The use of fractions as demonstrated by the Rhind
Papyrus and Akhmim Wooden Tablet, (2000 BCE) details the function and use of
Egyptian fractions as the basics of the ancient math system. We have abandoned
their demonstrated process it in favor of the simpler methods in use today,
failing to notice the concepts stated by the ancient’s methods. Using the
fractions based system of the Ancient Egyptians establishes a system based in
rational numbers.
2. Squaring the Circle Mathematically
Peter
Tompkins in “Secrets of the Great Pyramid” states, “The Pyramid is so
designed that for all practical purposes it accomplishes the squaring of the
circle. The Pyramid’s base is a square whose perimeter is equal to the
circumference of a circle whose radius if equal to the pyramid ‘s height”.
Imitate the Great Pyramid; Square the Circle as the
Great Pyramid demonstrates. After realizing this I find squaring the circle
mathematically a relatively simple process by applying the ancient’s methods.
The ancient’s method as demonstrated by the Great Pyramid shows that 1760
Royal Egyptian cubits are equal to the perimeter of the square and the
circumference of the circle. To obtain a side length of the square divide the
perimeter by four that yields a side length of 440 Royal Egyptian cubits. To
obtain the radius of the circle or height of the Pyramid the ancients used 44/7,
circumference 1760 / 44 * 7 = 280 Royal Egyptian cubits. Dividing these numbers
by ten will yield the ancient formula for squaring the circle. That being
One-hundred and seventy-six units equal the circumference of the circle,
Forty-four units equal the side length of the square and Twenty-eight units
equal the radius of the circle. This may not agree with our present system, but
the ancient builders were not cognizant of the system in use today, were they?
The ancient mathematicians demonstrated the simple but brilliant method for squaring the circle, multiply everything by four, the circumference becomes (44 * 4 = 176), the radius (7 * 4 = 28), the diameter (14 * 4 = 56) allowing for the side length of 44 units. This process in turn relegates 44/7 to the inherent value within the formula while giving the value for Base to height ratio of 11:7 producing an angle of 51° 50’ 33.98”. Occam’s razor states ”All things being equal, the simplest solution tends to be the best one”. " In simple English “The theory that describes the most things from the least assumptions is the best theory.”
3. The Royal Egyptian Cubit
20.62 inches is presumed to be the standard unit of measure for the Great Pyramid, this is an erroneous figure based on the fact it does not conform to the ancient’s methods, the correct figure for the Royal Egyptian cubit is as an Egyptian Fraction (1+1/2+1/5+1/55 feet) if we are going to be exact. This being equal to 189/110 feet or 20 34/55 inches written as 20.618181818… inches in decimal form. A Royal Egyptian Cubit of 189/110 * 440 gives a base length of 756 feet. To verify this figure for the Royal Egyptian Cubit I used the following logic. The Pyramid perimeter base of (756 * 4) equals 3024 feet. Using the ancient’s circle formula described above produces the following:
(3024 / 176 = 17 2/11 feet (17+ 1/6+1/66 feet) or (206 2/11 inches)
This dimension equals the width of the Kings Chamber within .004 inch of J. H. Cole’s measured width as noted in his 1925 Survey Paper # 39, dividing by ten verifies the length of the Royal Egyptian cubit to be 20 34/55 inches. By rounding numbers we miss the ancient’s concepts, using fractions eliminates this possibility.
4. Pyramid
Cubit
The true value of the Pyramid
cubit is (1 + 91/125 feet or 216/125 feet) 1.728 feet, having an Egyptian
Fraction equivalent value of (1+1/2+1/5+1/36+1/4500 feet) There are 440 cubits
per side in the Socket base (760.32 feet) multiplied times four then equals one
half mean geographic minute with a value of 3041 7/25 feet. A simpler way of
stating this is The Pyramid cubit is 176/175 of the Royal Egyptian Cubit. The
Pyramid Cubit gives a base length of 756 feet or 437½ cubits in the perimeter
of 1750 units. Demonstrating a 1760/1750 ratio relating to the Great Pyramid’s
measured base.
5. Ratio of the ancients
An excellent example of this Ratio for the units of measure is eloquently explained by John Michell in New View Over Atlantis where he discusses at length the ancients’ use of the ratio 175:176 regarding the units of measure The evidence of this ratio propelled by His discussions define the true working relationship of the ratio in the ancient system of measures derivations through the process of dividing by 175 multiplying times 176 to achieve the various units of measure used by the many ancient cultures. The only question that was not answered is why ancients use these numbers175/176? What concept, principle or element of the ancient’s system was determining factor for the use of these particular numbers? By the use of the formula for squaring the circle, we know the why; the circumference of any circle by ancient standards is equal to 176 units.
6. The Third Option to π and Φ, Squaring the Circle Geometrically
We have tried to remake the ancient structures to fit
within the concepts and elements established by our current system of
mathematics, neither π nor Φ, being rational numbers, could be the
design element governing the construction of the Great Pyramid. While our values
for π and Φ both offer suitable credentials for the task, neither
offers insight into the concepts and principles of the ancients, failing to give
us what we really desire… real and verifiable answers.
The Third option, the one designed by the ancients to express their concepts principles and elements is the basic 1/7 angle of 51 3/7°. Reputed to be a sepentary culture the one-seventh angle would be the logical choice. Logically, the inability or our system to square the circle obscures the concepts and elements the ancients incorporated within the structures using the squared circle. The real question is can we verify any findings to a point beyond any doubt?
The figure 1 drawing illustrates a construction that for all practical purposes completes the squaring of a circle, with the perimeter of the square being equal to the circumference of the circle with the about same degree of accuracy as 22/7 relates to the value of π in our system. This construction (figure1) was created with a compass and a straight edge, produces the subsequent results: Lines AF, BE, BH, CG, CJ, DI, DL land KA being 1/7 segments of a circle derived using the formula encoded on the Giza Plateau. The one-seventh angle revealed the basis of the ancient’s design formula for the Great Pyramid and defines the remaining concepts, principles and elements used in the construction of this ancient structure.
There is an exhibited and repeatable construction formula contained within the structures of the Giza Plateau defining the seventh angle and other components of the Constructions. The seventh angle coupled with the mathematical formula from above give credibility to the idea that the Great Pyramid is the Repository of ancient knowledge with a message from the ancient builders. The message of the seventh angle, squaring the circle both mathematically and geometrically encoded within the ancient structures of the Giza Plateau and the Great Pyramid. Proof’s for these formulas are too lengthy to address in this article but can be provided upon request.
Figure 2 demonstrates the finer points of the geometric construction where the 56th portions define the corners of the square and its relationship to the circle at the points of intersection, the points 6/56 = 38 4/7°, 7/56 = 45° and 8/56 = 51 3/7° illustrates the corner of the square of the northeast quadrant, just as points 20/56 = 128 4/7°, 21/56 = 135° and 22/56 = 141 3/7° illustrates the southeast corner; points 34/56 = 218 4/7°, 35/56 (225°) and 36/56 = 231 3/7° illustrates the southwest corner; points 48/56 = 308 4/7°, 49/56 = 315° and 50/56 =321 3/7° illustrates the northwest corner creating a squared circle geometrically whose perimeter is equal to the circumference of the circle accurate within the limits established by the Great Pyramid. This is the same formula present at and used by the ancient Britton’s to construct Stonehenge.
What standard of measure did the ancient’s actually use? I will let you
be the judge on this one. The Earth is to some extent oblate; its radius at the
equator is larger than its radius along the rotational axis. Additionally there
are irregularities in the surface because of hills, mountains, valleys et
cetera.
The Earth's mean radius is
determined as the average distance from the physical center to the surface,
based on a large number of samples. This is roughly 3,960 statute miles.
(V = (4/3)(π) r3) For Earth, the volumetric radius equals 3,958.690909…Statute miles (20901888 feet) this Ancient figure is within 2 miles of today’s preferred figure.
John Michell states in New View Over Atlantis on page 130 demonstrates the equation as shown below using feet as a basis for this equation. Logic would dictate that if the radius is equal to seven and the circumference is equal to forty-four then the sequence would lead to the equation of foot derivations for the Earth’ mean dimensions. So in raw numbers without any preconceptions using no units of measure only the Ancient’s value 44/7 as a source of these numbers gives the following equation:
(44*12=528) (528*12=6336) (6336*12=76032) (76032*12=912394) (912384*12=10948608) (109486308*12=131383296) = (44 * 12^6 = 131,383,296 feet) = Earth’s mean circumference in feet.
What was not demonstrated is the Royal Egyptian cubit of 179/110 feet or 189/110 feet in the inverse 110/189 following the same formula as above yields the following:
(110/189
* 12 = 6 62/63) (6 62/63 * 12 = 83
17/21) (83 17/21 * 12 = 1005 5/7)
(1005 5/7 * 12 = 12068 4/7) (12068
4/7 * 12 = 114822 6/7) (114822
6/7 * 12 = 1737874 2/7) (1737874
2/7 * 12 = 20854491 3/7 feet) =
(110/189 * 12 ^ 7 = 20854491 3/7 feet) = Earth’s Polar Radius in feet.
Suggesting the Royal Egyptian Cubit as being more than just a unit of measure, but a designed unit with a multiple purposes in mind.
The use of 44/7 establishes the mean dimensions of Earth respectively and the British Foot confirmed, by the above equation, as the preferred unit of measure of the ancient builders. Concluding the dimensions of the Earth as used by the ancients’ and derived by the above formula eliminates the possibility of the numbers for the dimensions of Earth being arbitrary.
The ancient mathematicians used these formulas as a
standard method to derive all of the numbers used within the matrix of their
geodetic system. Thus you can say that the Earth’s mean circumference of (44 *
12^6) 131383296 feet divided by 5280 equals 24,883.2 miles
(12^ 5 / 10 miles).
The Earth’s circumference of 131,383,296 feet
divided by one side length (756 feet) of the great Pyramid equals 1737874 2/7
(110/189 * 12 ^ 6) or 10,000 cubits of 1.7378742857142857… feet, equal to a
12,000,000 part of the Earth’s Polar Radius equal to the basic unit of measure
of Stonehenge. Yes again, Stonehenge can be linked to the Great Pyramid by many
different methods, but that is for another time or article.
The above information results from using the ancient concepts and basic mathematics i.e. addition, subtraction, multiplication and division to resolve many of the questions that have gone unanswered. This would be supported by the mainstream archaeologies belief the ancient cultures were incapable of advanced mathematics, or were they? Further study will demonstrate the ancient builders were far more advanced then we could imagine. This statement is based on the many theories expressing the structures demonstration of the functions of higher mathematics. Are these theories coincidence, naturally occurring or planned features within the structure?
Conclusions:
I am in high regard for the genius demonstrated by
the Giza Plateau and in the Great Pyramid even after millennia these structures
are still capable of conveying messages from the ancient builders. The
information presented here illustrates the likely planned design elements of the
Great Pyramid, allowing for the extrapolation of the true definitive dimensions
for the structure, with a seventh angle being the foundation for the concepts,
principles and elements governing its construction. It also presents the basics
of the Ancient geodetic system as being analogous to our own. This information
is powerfully indicative of the Pyramid’s true purpose as a mathematical
dissertation representing the ancient’s concepts, principles and elements,
making the Great Pyramid more comparable to a mathematical time capsule, rather
than the mausoleum or burial chamber as today’s Egyptologist would have you
believe.
This quick glimpse of the ancient’s concepts demonstrates that by returning to the basics and making the fewest assumptions possible, the Great Pyramid provides abundance information, such as squaring the circle both mathematically and geometrically. Provides formulas for deriving units of measure such as cubits and the foot. Many different people, to the point it has almost become an established fact, have confirmed the basic unit of measure of the ancient’s to be the British Foot. As the source of the British foot the inch has to my knowledge has never been defined, but using the ancient methods has established the source for the inch as a derived unit of measure, but because of space restrictions of this article will have to wait for another time.
I am not saying this Hypothesis is the last word relating to the construction elements of the Great Pyramid. I am saying it is the simplest explanation put forth to date, the Great Pyramid by Cole’s survey # 39 generates the formulas and numbers worthy of additional evaluation.
”All things being equal, the simplest solution tends to be the best one” William of Occam.
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© 1988-2007
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Rights Reserved
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portion of this Document may be reproduced with out written consent
Albuquerque,
New Mexico Email:
boaz.jacob@gamail.com.
Sources:
John
Michell “New View Over Atlantis” Published by Harper and Row Publishers,
Inc. 1983
J.
H. Cole “Determination of the Exact Size and Orientation of the Great Pyramid
of Giza” Published by Government Press, Cairo
(Survey
of Egypt Paper no. 39)
1925
Peter
Tompkins “Secrets of the Great Pyramid” Published by Harper and Row
Publishers, Inc.1978
Charles
Piazzi Smyth “The Great Pyramid” Published by Bell Publishing Company 1990
Lehner,
Dr. Mark, "The Complete Pyramids", Thames& Hudson
W.R. Fix “Pyramid Odyssey” Published by Mayflower Books 1978