Hi All,

The purpose of this presentation is to demonstrate the Ancient Egyptians mathematical concepts and principles and elements will not translate using the concepts from our current system of mathematics. Attempting to use Greek concepts such as pi, phi and square root of two (irrational numbers) and the meter to research the concepts of the Ancient Egyptians only propagates the "I can't see anything there, so there isn't anything there to see." Logic, and the pyramids continue to defy comprehension because the Greek concepts, the meter and base 10 decimal system we currently employ are incapable of proper translation of the concepts, principles and elements of Ancient Egyptian mathematics.

What design parameters are responsible for the size of G1? A design parameter is an idea that begins on paper with the help of a pencil or pen. If I wanted to create a structure to relay mathematical ideas one would of course start with the simplest concept capable of relaying the idea without margin for error. There is nothing simpler than 1,2,3,4,5,6,7,8,9, add unit fractions and move on to the more complex concepts principles and elements of the system. Is this simple method how the Ancient Egyptians approached the design of the Great Pyramid.

In the RMP there are 84 fractional problems some of them are algebraic problems that use unknown variables and accordingly they were deciphered using unit fractions and division-by-ten along with other basic arithmetic. They employed a concept we call the "Eye of Horus," in which different portions of the hieroglyph symbolize the different fractions with a numerator of one and a denominator based on the powers of two: (1/2, 1/4, 1/8, 1/16, 1/32, 1/64) equaling 63/64. The Old Kingdom numeration system employed a cursive binary algorithm that basically rounded off a 1/64. By using 63/64 instead of the 64/64 unity, as shown in Milo Gardner’s [independent.academia.edu] equation ((64/64)/n = Q/64+5 R/n, * 1/320), with the powers of two enabled them to perform multiplication, division and algebraic problems using addition and subtraction. He states: Old Kingdom arithmetic was written in an infinite series system that rounded off unity (1) = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 ... by throwing away a 1/64 unit. The rounded off binary numeration system was "healed" in hieratic Egyptian fraction mathematics. So I have to ask did the New Kingdom numeration system repair or obscure the intent of the Old Kingdom Scribes?

The old kingdom is time period during which the greatest of the pyramids were built using the Eye of Horace in the form of 63/64 and the practice of multiplying or dividing by 10, 100, or 1000 etc. since these numbers are demonstrated by the hieroglyphs. What is present in the various papyri are known quantities, while many of the unknown concepts, principles and elements of Ancient Egyptian mathematics linger in obscurity. It should be noted the Rhine Mathematical Papyrus, Moscow Mathematical Papyrus, Akhmim Wooden Tablet are an abbreviated form of modern mathematical statements.
I then realized and I am noting that (63/64)/n = Q/63+5 R/n, describes or defines a hyperbolic paraboloid geometrically, [en.wikipedia.org] plotting the solution R = (3969-64 n Q)/20160, n!=0, undoubtedly yields a hyperbolic paraboloid.[en.wikipedia.org] The other elements of their system the Scribes thought of and did not document on papyrus should unquestionably reside within the structures they built.

I could be wrong but this is what I see:
Once in awhile something so simple comes along and is the embodiment of Occam’s razor. In this case it is that simple something defines the dimensions of G1, Sun, Earth Moon. I am surprised no one has explored the fact that 1x2x3x4x5x6x7x8x9 = 362880 in relation to G1. If I had to offer a reason it would be because no one really believes the Ancient Egyptians employed the inch as a unit of measure and therefore has been wholly ignored. That is about to change!

What is the significance of the number 362880? It is: 9!
Table[n!, {n, 9}]
n |
1 | 1
2 | 2
3 | 6
4 | 24
5 | 120
6 | 720
7 | 5040
8 | 40320
9 | 362880


For one it is ten times the base perimeter of G1, 1/10 x 362880 = G1’s perimeter base in inches.
Then 362880 / 4 = 90720, 90720 / 10 = G1 side’s base in inches. In order to determine the height of G1 we use the following formula of a 5 1/2 seked which would be 14 rise to 11 run, giving the following: 9072 / 2 / 11 x 14 = 57730 10/11 inches divided by 10 = G1 height.

Further divided by 5 yields 362880 / 5 = 72576, which is twenty times the perimeter of G1 in inches manifest within the figures. Factoring 72576 /12 = 60480 = 20 x G1 perimeter in feet.

Included is 362880 / 6 = 60480, 20 x G1 perimeter in feet.

Further it is possible to extrapolate 362880 / 7 = 51840, which is approximately 1000 x the angle for G1 in degrees.

362880 / 8 = 45360, of which 1/10 of 45360 is the 1/2 base of G1 as divided into 8 segments by the centerline inset along G1 base line as noted by Petrie.

Dividing 9! times the number of cubits in G1 dimensions yields the following values:
Perimeter 362880 / 1760 = 206 + 1/6 + 1/66 inches width of the Kings Chamber (206 2/11 inches)

Base 362880 / 440 = 824 + 1/2 + 1/8 + 1/11 + 1/88 the length of the Kings Chamber doubled (40 cubits)

Height 362880 / 280 = 1296 equal to the number of inches in the perimeter of the Kings chamber North wall which is 10 x 2 pi cubits according to Petrie the circumference of a circle with a radius of 10 cubits of 20 + 1/2 + 1/10 + 1/55 inches or 20.61818181… inches. (1296 / 44/7 = 206 2/11)

Building a case for the number 5280 and the Ancient Egyptians:
(Table[n!, {n, 9}])/5280
{1/5280, 1/2640, 1/880, 1/220, 1/44, 3/22, 21/22, 84/11, 756/11}

362880 / 5280 = 68 8/11 (68 8/ 11 x 7 = 481 1/11 the number of feet height G1) (68 8/11 x 11 = 756 the number of feet in the base of G1) based on the 5 1/2 seked demonstrated by G1. The vulgar fraction expressing this same value is 756/11.

The number 9072 relates to 5280 in the following manner, it is equal to 189/110 when if taken as feet equals (1.71818181…feet) equal to the Royal Egyptian cubit in feet: therefore, (1 cubit) 189/110 x 5280 is 9072 square feet equal to 1/63 the base area of G1, 9072 x 63 = 571,536 square feet, 571,536 / (189/110 ^2) = 193,600 square cubits (440^2) or 19 9/25 (22^2 / 25) aurora. A strip of land 63 statute miles long and 1 cubit wide is equal to the base area of G1. Therefore: 5280 x 63 x (14/11) x (99/70) / (22/21) = base area G1.

So what exactly is the cubit? A good definition the cubit is one foot (12 inches) times the rise run of G1 (14/11) times the rational value of the square root of two (99/70) divided by the hyperbolic ratio ((22/7) /3) or as the Ancient Egyptians used it 22/21
The cubit by concept is in rational terms: One British imperial foot x 14/11 x 99/70 / 22/21 = 189/110 feet. Doing the same in inches we find: 12 inches x (14/11) x (99/70) / (22/21) = 20 34/55 or 20.6181818… inches.

<[www.grahamhancock.com];

Rise-run^2 x rational sqrt 2 / pi/3 x 5pi = (1x2x3x4x5x6x7x8x9) / (5280x2)
(14/11)^2×(99/70)/(22/21)×(5*22/7) states conceptually what is stated mathematically as 362880 / (5280x2) equal to 34 4/11 the length of the Kings Chamber in feet.

Earth dimensions:
Having established n^2 /63 was demonstrated in area of the pyramid G1 will generate the radius of the Earth using the same equation (n^2 / 63). Just as demonstrated by the base area of G1 440^2 / 63 reveals its secrets, find that (1x2x3x4x5x6x7x8x9) ^2 / 63 = 2090188800 which is 100 times the Earth’s Mean radius. 2090188800 / 100 = 20901888 feet or 3958 38/55 miles (a figure NASA puts at 3958.8 miles) of 5280 feet further: 7 x 12^6 = 20901888, 7 x 12^6 x 6 x 22/21 = 44 x 12^6 =131383296 feet the Earth’s mean circumference. Demonstrating a correlation between the dimensions of G1 and the Earth dimensions from the same numbers by a simple mathematical equation all answers in feet and inches.

Adding to the evidence, the inverse of the Royal Egyptian cubit multiplied by 12^7 is equal to the Earth’s Polar radius, 110/189 x 12^7 = 20854491 5/7 feet, this and all above offers strong evidence the pyramid builders were aware of the Earth’s dimensions.

Moon dimensions:
Just a couple more calculations: 1x2x3x4x5x6x7x8x9 x 220/7 (10pi) = 11404800 this equals the number of feet in the Moon’s diameter (a figure NASA puts at 2159.2 miles) was calculated as (362880 x 220/7 /5280) = 2160 statute miles.

Sun dimensions:
1x2x3x4x5x6x7x8x9 x 88000/7 (4000 pi) = 4561920000 the diameter of the Sun in feet. (4561920000 / 5280 = 864000 statute miles) (a figure NASA puts at 864337.2 miles).
Curve the Suns diameter into a circle place the sphere of earth within that circle and allow the Earth, while spinning, to circumnavigate the circle of the Sun, what is found is for every second of Earth rotation (1520 16/25 feet) the equivalent distance covered on the Sun Circle is equal to 52800 feet at a ratio of 1: 34 13/18 (or expressed as a vulgar fraction of 625/18) Earth mean circumference 131383296 x 625/18 = 4561920000.

Stating the obvious, using 1x2x3x4x5x6x7x8x9 will not only generate the dimensions of G1, but by the application of simple mathematical concepts will generate dimensions of the Sun, Earth and Moon, which will further serve to demonstrate that Scribes did not always record other prerequisites of the Ancient Egyptians system of mathematics thought of on the papyrus.

Again the base area of G1 is 63 x 5280 x (14/11) x (99/70) / (22/21) and is purely mathematical in nature. How to transmit information across millenniums there has to be a method to decode what was encoded and that method seems to be simply 1x2x3x4x5x6x7x8x9.

What happens if we replace 63 with 64?
Then 362880 / 64 = 5670 inches 472 1/2 feet, 275 cubits the base of Meidum pyramid at Saqqura gives a perimeter of 1890 feet or 1100 cubits (1890/1100 = 189/110 the Royal Egyptian Cubit.) But Meidum Pyramid and 64 is a subject for a different time so I will stop here.

What is demonstrated is the difference fractions make in recognizing Ancient Egyptian concepts and very strong evidence for the use of rational numbers, the British Imperial inch, foot and statute mile as the design units of measure employed in G1. It seems to be a statement defining G1 along with many other undiscovered things regarding the world in which we live. Based on the conceptual mathematics of the Grand Gallery and Kings chamber within G1, I have no reason to doubt this what is shown above is correct.
[www.grahamhancock.com]
Their statement is: ‘we were here and this is what we knew, if you want to know start here: 9! / (5280 x2) = 34 4/11 (378/11 feet)
378/11 x 22 = 756 feet ………….base G1 440 cubits
378/11 x 21 = 721 7/11 feet.…….base Red Pyramid 420 cubits
378/11 x 18 = 618 6/11 feet……. base Bent Pyramid 360 cubits
378/11 x 11^2/12 = 346 1/2 feet.. base G3 201 2/3 cubits

Regards