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TTHHEE
CCOOMMPPUUTTEEDD
TTHHRREEEE LLEENNGGTTHHSS
OOFF TTHHEE GGRREEAATT PPYYRRAAMMIIDD BBAASSEE
““SSTTOONNEESS OOFF TTRRUUTTHH””
GGIIZZEEHH
11
MM.. SSaabbeett Delft–Holland
March 2004
YOU CAN UNLOCK ALL DOORS IF YOU ONLY HAVE THE KEY
AND THE KEY IS ALLWAYS WITH GOD
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
2
TTOO TTHHEE AALLMMIIGGHHTTYY OOUURR DDEEAARR LLOORRDD AANNDD TTOO HHIISS BBEELLOOVVEEDD HHOOLLYY LLAANNDD MMAASSRRÉÉLL11
TTHHEE MMOOTTHHEERR OOFF TTHHEE HHEEBBRREEWWSS,, TTHHEE AARRAABBSS AANNDD TTHHEE AALLLL NNAATTIIOONNSS
II PPRREESSEENNTT HHEERREE PPAARRTT OOFF MMYY IINNSSPPIIRREEDD WWOORRKK
MM.. SSAABBEETT
DDEELLFFTT––HHOOLLLLAANNDD
1 MASRÉL is the Semitic name of “Egypt” in ancient Egyptian language, which is the equivalent of the biblical adopted name
MISRAIM and the present Arabic name MASR.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
3
HE WHO
CAN UNRAVEL THE MYSTERY
WILL BE SHOWN A SYSTEM FUNDAMENTALLY
APPARENT IN NATURE-REVEALING CYCLES, PROPORTIONS,
DISTANCE, TIME, AND MEASURES, IN RELATION TO MAN AND HIS WORLD
C. Staniland Wake
© M. Sabet, 2004 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including
photocopy, recording or any information storage and retrieval system, without permission in writing from the author. [email protected]
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
4
CONTENT
ABSTRACT 5
INTRODUCTION History 6
Knowledge 6
Purpose 7
The DAUL QUADRATIC FORMULA OF THE GREAT PYRAMID OF GIZEH The dual quadratic formula 8
The hollowing effect 9
Davidson’s assumption of the Great Pyramid three base lengths 10
The quest 10
SOLVING THE RIDDLE OF THE THREE BASE LENGTHS The mutual link between inner and outer design 11
The three inner distances and the three base lengths 12
The three lengths of the Great Pyramid base 14
EVALUATION OF THE GREAT PYRAMID COMPUTED RECORDS Geodetic Datums 15
Geodetic Reference System Ellipsoid 1980 (G.R.S.’80) 15
The proportion of 1/43,200 15
The Great Pyramid base is 7.5 second of degree latitude at 30° north 16
The length of the land of Egypt is 7.5 degree latitude 16
Scale proportion of 1:3600 16
CONCLUSION 17
Appendixes 1
The Egyptian Book of “CCOOMMIINNGG FFOORRTTHH BBYY DDAAYY IINN TTHHEE UUNNDDEERRWWOORRLLDD” 18
Number 4601200 and the Golden Section Proportion 18
Divinity of the Number 4601200 19
Calculation of the Great Step–South Wall distance 19
Appendixes 2
THE GEODETIC REFERENCE SYSTEM ELLIPSOID 1980 21
The Earth Great Circle of the Great Pyramid 22
Bibliography 23
Illustration credits 23
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
5
ABSTRACT
This article is a small part of a wider research that opens the true ‘Golden Gate’ to explore the
architecture code of the Great Pyramid of Cheops by means of the Golden Section proportion. The
genial tool used for this breakthrough is a composed quadratic equation invented by the author in
1987 on his study of the Great Pyramid. This unique formula I named ‘SSAABBEETT EEQQUUAATTIIOONN’ or the ‘DDUUAALL
GGOOLLDDEENN SSEECCTTIIOONN FFOORRMMUULLAA OOFF TTHHEE GGRREEAATT PPYYRRAAMMIIDD’’ as follow:
± a F0 2 ∓ bF0 S0 ∓ cS0
2 = 0
As a unique architecture key; this formula has successfully solved many of the various puzzles of the
inside as well as of the outside mysterious structure of the Great Pyramid of Gizeh.
For instance, one of the unsolved puzzles up till now is: How to identify and calculate the three
different lengths of each side at the Pyramid base due to the hollowing effect or concavity of each
face of the Great Pyramid.
The hollowing effect or concavity of the Great Pyramid faces was detected by Sir Flinders Petrie
(1853-1942) during his survey of the Gizeh plateau.
In 1924 David Davidson announced that each concaved face of the pyramid would create three
different lengths at each side of the Pyramid base, see figure 3, 4. Moreover, Davidson stated that
these three different lengths at the base would describe and match the three different years
known to us as the solar, the sidereal, and the anomalistic year. Since then, there is no further
investigation on the subject perhaps because of the completely lost evidence of the Pyramid casing
stones.
Although the author thinks there was at least one more length undetected by Petrie or Davidson
because of the lost traces of the Pyramid casing. This undetected length would represent the lunar
year and its relationship with the other three years mentioned by Davidson. Yet, this manuscript will
introduce only the three calculated lengths of the Great Pyramid base according to Davidson’s
assumption for the three different years named by Davidson.
The calculated shortest length of the Great Pyramid base has proved to join very accurately the
distance and time of the earth rotation around its axis. Compeered with the data of the American
Geodetic Reference System ellipsoid 1980 of the earth survey, this shortest calculated base has
shown the accuracy of the second of degree length at 30° latitude (the small circle) coded in the
Great Pyramid base. Details of mathematical and geometrical analysis are omitted in this article for
security reasons. Further study on the subject will unlock more significant records of Cheops Great
Pyramid as yet still unsolved.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
6
INTRODUCTION
History Assigned exactly at 30° latitude from the earth equator by the Egyptians thousands of years ago
before the Greenwich to signify the focal geometry of the Egyptian Delta, distant 16 Kilometres
southwest from the centre of Cairo, there on the bedrock of the Gizeh plateau stands the Great
Pyramid of Egypt. As the most majestic and mysterious monument ever erected by man on the
face of earth, the Great Pyramid is the largest stone building and last survived wonder of the
ancient world Golden Ages.
Each of its four faces was dressed by 5.5 acres2 of marble-like casing stones; weighed at times
more than ten tones apiece. The casing polished stones has shone glitteringly beneath the rays of
the Egyptian sun earning the splendour of their edifice identity as “KKHHEEUUTTYY” meaning “TTHHEE LLIIGGHHTT”.
Legends told that Thoth (known as Hermes by the Greeks) is the one designed the Gizeh Pyramids
before the Flood to preserve the knowledge and secret science of ancient Egypt. At the Gizeh
Plateau, Thoth coded and sealed in his Grand Design the past wisdom and golden science using
elemental science for a future generation remote to come.
The Greek historian Herodotus who visited Egypt in the fifth century BCE, has reported inscriptions
of strange characters painted and carved on the pyramid’s casing stone.
Under the command of Caliph Al-M’amun of Baghdad in 820 AD, Arab workers had forced their way
into the Great Pyramid through the north face. The Arabs caused atrocious damage to the Pyramid
irreplaceable casing structure and carved hieroglyphics. The historian Arab Abd Al-Latif in 1179 AD
confirmed that, the inscriptions painted on the Pyramid casing were so numerous that they could
have filled "more than ten thousand written pages” of ancient Egyptian knowledge and wisdom.
Sadly, in 1356 BCE, followed by an earthquake the Arabs robbed the remnant of the Pyramid
casing stones to build their mosques and fortresses in Cairo. Cut into smaller pieces, reshaped and
polished, all recorded and carved treasures of this ancient unique library were lost forever.
The Arabs even attempted to disassemble and breakdown the Great Pyramid itself, however after
removing 30 feet of its stones at the top; they gave up this savage impossible task.
Yet, seeking an architecture clew in the Great Pyramid always motivates one to ask himself. Is this
lost knowledge of the casing stones destroyed by the Arabs are the only information recorded in the
Great Pyramid? Or, there are other traces still treasured and hidden within the design?
Knowledge It is well known to intellectual scientists that the Great Pyramid of Gizeh is not a royal tomb as
some still claim, but it contains superior knowledge of geometry, mathematics, physics, geodesy
(science of earth survey), astronomy, et cetera. Only during the second half of the 20th century,
modern science has approached the technology which made it possible to recognize the astounding
universal knowledge documented by the Egyptians in this Grand Design.
Recently, it is confirmed that the Great Pyramid is aligned with the earth’s four cardinals more
correctly than any modern building including the Meridian Building at the Greenwich Observatory
in London.
2 Acre: measure of land area, is now fixed as 10 square chains or 160 square rods, i.e., 4,840 sq yd, 43,560 sq ft, or 1/640 sq mi.
It is equal to about .4047 of a hectare or 4,046.9 sq m.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
7
In 1970s, modern scientists obtained for the first time the most reliable earth measurements by
means of the space survey of the American satellite. These modern measurements in fact are as
accurate as those contained in the Great Pyramid structure thousands of years ago.
In some other researches it is found that the Pyramid base is situated at the centre of the
earth's landmass. This mean that, the latitude and longitude lines on which the Pyramid is centred
passes through more land and less water than any other latitudes on earth. Moreover, the north-
south meridian of the Great Pyramid divides the earth into two equal halves regarding water and
land surfaces. Finally, I found in 1986 that the complete Pyramid simulating the earth northern
hemisphere on a scale of 1:43,200.
The question is now, why all these advanced knowledge and distinguish facts was implied in the
Great Pyramid and the Gizeh Plateau? Up till now there is no clear answer, yet, modern science
still searching to decipher this coded science of past Golden Edges, which might reveal one day
some of the advanced knowledge from the past and we do not know yet.
Purpose No other monument on earth was measured, surveyed and checked so often and with so much care as
the Great Pyramid of Egypt. The edifice that was built so perfect and yet so enormous that its
enigmatic structure and accuracy would challenge even today’s technology almost to a breaking point.
The mysterious design of the Great Pyramid has drawn scientists’ attention from different fields of
science in an attempt to solve its architectural mysteries. In the course of time and according to
their level of knowledge, scientists explored various data of the Pyramid records. However, as it is
always the case, the Great Pyramid still putting forward a new puzzle to be searched in order to
solve.
In 1924, David Davidson introduced his hypothesis to verify the hollowing effect of the pyramid’s
four faces which was detected by Sir Flinders Petrie. Davidson in his statement claimed that the
concavity of each face of the Pyramid would provide three lengths at each side of the base. The
three different lengths AB, AEFB, and AEbFB as in figure 4 would correspond to, according to
Davidson, the three lengths of the year as computed by modern science, the solar, the sidereal, and
the anomalistic year3. Academics of his time rebutted that all this was purely attributable to chance
and coincidence and nothing else!
Although the author is convinced that there were more than three different lengths for each side
of the Great Pyramid base, this report was designed to issue the THREE COMPUTED LENGTHS of the
Great Pyramid base according to Davidson’s assumption. The results of the calculated three lengths
as we will see in a later chapter are:
1. 230.9400 m
2. 231.4502 m
3. 232.2755 m
3 Solar year: is the exact observed time between two successive autumnal equinoxes, when the day is exactly as long as the
night. It is now 365 days, 5 hours, 48 minutes and 45.22 seconds, or in decimals: 365.242190. Sidereal year: is the time it takes a star to reappear in the same place in the sky for earth observer. It is about 20.41 minutes longer than the solar year, or 365.256363 days. Anomalistic, or orbital, year: is the time it takes the earth to return to the point in its elliptical orbit nearest the sun. This is about 4.71 minutes longer than the sidereal year, or 365.259635 days.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
8
The DUAL QUADRATIC FORMULA OF THE GREAT PYRAMID OF GIZEH
History tells that the key to the Great Pyramid architectural secrets was handed to Herodotus by
the Egyptian priests of Onnu Temple (Heliopolis). Analysing Herodotus’ report, Sir John Taylor
(1781-1864), concluded the Pyramid was designed in such a way that “TTHHEE AARREEAA OOFF EEAACCHH OOFF IITTSS FFAACCEESS
WWAASS EEQQUUAALL TTOO TTHHEE SSQQUUAARREE OOFF IITTSS HHEEIIGGHHTT”. This means the Great Pyramid was constructed by “THE
GOLDEN SECTION PROPORTION”, see figure 1. Applying Pythagoras theorem to the triangle (abc) it is
convenient to build up the next quadratic formula of the Golden Section (2) as follow:
2 = + 1 (1)
Or,
2 - - 1 = 0 (2)
Since the formula 2 - - 1 = 0, algebraically characterizes4 the arithmetic of the Golden
Section, it is convenient to call it “THE CHARACTERISTIC FORMULA OF THE GREAT PYRAMID”.
The dual quadratic formula
Analyzing the Great Pyramid geometrically, the author succeeded to invent the dual quadratic
formula (3) and called it “Sabet Equation” or “THE DUAL QUADRATIC FORMULA OF THE GREAT PYRAMID”
(DQFGP):
± a F0 2 ∓ bF0 S0 ∓ cS0
2 = 0 (3)
Whereas Fo and So are simultaneously mutual variables, and the scalars a, b, and c, are the
coefficients of Fo and Uo respectively.
This dual formula has successfully explained the architectural mysterious design of the Great
Pyramid unique structure. This dual formula has effectively uncovered many of the inner as well as
the outer architectural puzzles that were designed by the genialities of the Golden Section
perception in both the Great Pyramid and indeed in the Gizeh Plateau field.
4 A characteristic equation is a polynomial whose roots are eigenvalues.
1. The area of each face of the Pyramid is equal to the
Pyramid square height.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
9
The hollowing effect
One of the remarkable features observed on the Great Pyramid four faces is the hollowing effect
or concavity of each face. The core masonry of the Pyramid four faces is concaved at the centre
of each face with an extraordinary degree of precision as in figure 2 and 3. The hollowing-in of the
Pyramid faces is invisible to the human eye without instrumental observation; however, nowadays it
can be seen from the air at certain times in the daylight. In 1940 the British Air Force pilot, P.
Groves was the one noticed this phenomenon and captured it in the now-famous photograph of
figure 2.
The concaved faces of the Great Pyramid were also discovered by Sir Flinders Petrie (1853-1942).
Petrie5 noted a distinct hollowing of the core masonry at the centre of each face of the Pyramid, he
noticed: (continually observed that the courses of the core had dips of as much as 0.5° to 1°).
Although the sum of the hollowing is 0.94 m (37 inches) at the centre of the Pyramid north face.
Petrie found no evidence at all of the hollowing effect along the lower level of the Pyramid base
because it is completely vanished.
5 The Pyramids and Temples of Gizeh, Field & Tuer, London, 1883, page 421.
A
E
F
B
G
H
C
ac db
The magnified hollowing effectof the Great Pyramid core masonry
© M. Sabet-2003
3. The hollowing effect of the Great Pyramid faces
exaggerated and the depths of the courses magnified.
2. Airial view of the Great Pyramid showing clearly
the hollowing effect at the middle of the western
and eastern faces, which was discovered accenedtly
by British Air Force piolt, P. Groves in 1940.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
10
Davidson’s assumption of the Great Pyramid three base lengths
Discovering the concavity of the Great Pyramid faces prompted a new theory; Davidson in his book6
‘The Great Pyramid its divine message’, stated: “the hollowing effect would give three basic lengths
of the year as recorded by the ancient Egyptians in the base of the Great Pyramid”. Figure 4, shows
Davidson’s assumption for the Great Pyramid three base lengths of each side as follow:
1. An outer or shorter length (AB), from corner to corner, bypassing the hollowed casing.
2. A second length (AEFB), slightly longer, along the casing stones of the base hollowed face.
3. A third length (AEbFB) longer than the second, who includes the entire angle within each
hollowed face.
These three measures presented by the ancient Egyptians in the Great Pyramid base; according to
Davidson, could have given the equivalents of the three periods of the year as computed by modern
science which are:
1. The solar year
2. The sidereal year
3. The anomalistic year
In my view, if this will prove to be the case, then, Davidson’s attempt will be the first of its kind to
combine Distance, Time, and Speed of the earth orbits around its axis and the sun in the Great
Pyramid dimensions.
The quest
The quest is to calculate the three lengths of the
Great Pyramid base. Still, if we remember the
fact that the Pyramid casing stone is completely
lost, such quest seems to be an impossible task to
approach. Nevertheless, the curious system of
chambers, corridors and the high degree of
precision used in the Great Pyramid inner design
might be the key solution to the quest. Only in
one case, if and only if, there is a design or
length relationship between the inner and the
outer architectural plan of the Great Pyramid
construction.
In this case, if there is such planned link, then,
how to solve this new architectural enigma? How
to compute the three various lengths of the
Pyramid base through all or part of the inner
designed structure?
Such enquiry led the researcher to study the
unusual structure of the Great Pyramid with a
new perspective.
6 The Great Pyramid, its divine message, Williams and Norgate, ltd, London, 1948.
A B
CD
L M
NO
E F
G
H
JK
P
R
12 3
4
5
6
a
b
c
d
12
11
710
"12345.....12" is the base of the core masonry"LMNO" is the base as actually built
AEFBGHCJKDPR is the casing stone limits at the base© M. Sabet 2003
89
4. Illustration of Davidson’s assumption of the Great
Pyramid three base lengths AB, AEFB and AEbFB.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
11
SOLVING THE RIDDLE OF THE THREE BASE LENGTHS
The mutual link between the inner and the outer design
One of the architectural facts that were discovered during my study on the Great Pyramid, which
still unknown to scholars on this subject is the mutual relationship between the inner and the outer
lengths of the Great Pyramid design. All the three-dimensional lengths of the Great Pyramid inner
and outer structure are related harmoniously to each other. As outcome of this breakthrough are
the three computed lengths of the Pyramid base by applying my invented Dual Quadratic Formula of
the Great Pyramid:
± a F0 2 ∓ bF0 S0 ∓ cS0
2 = 0
Applying the geometrical solution of the Dual Quadratic Formula to the Great Pyramid meridian
triangle, see figure 5. It was possible to formulate three equations each illustrates the mathematical
and geometrical relationship between one of the three inner distances and the half base length (B)
of the meridian triangle. The three inner distances involved are contained in the distance between
the Great Step of the Grand Gallery and the South Wall of the King Chamber (distance C0 C-2),
figure 5.
The Great Step; is the transition point between the upward climb of the Grand Gallery and the
horizontal platform that leads to the final passage to enter the Kings Chamber, figure 6.
Solving the three formulas provides three different lengths to the Great Pyramid half base (B), as
we will see next.
0-1-2
M. Sabet2003
N
0 15 m
GreatStep
C C C
6. The geometrical solution (C-1) divide the
distance Great Step-south wall (CoC-2) into
two distances (C0C-1) and (C-1C-2).
C C C0-1-2
M. Sabet / 2003
500 100 m
N
B
5. The geometrical solutions C0, C-1, and C-2 of the Daul
Quadratic Formula of the Great Pyramid.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
12
The three inner distances and the three base lengths
The three solutions of the Pyramid Formula are, see figure 5:
1. (C0)
2. (C-1)
3. (C-2)
Obviously, the second solution (C-1) divides the distance of the Great Step-South Wall (C0C-2) into
two distances (C-1C0) and (C-1C-2).
The measured7 figure of the distance (C0C-2) by Sir Flinders Petrie is 13.6459 ± 0.0228 m, or
537.239 ± 8976 British Inch.
I calculated the same distance (C0C-2) as 13.6595 m, or 537.7745” British Inch from the Egyptian
Book LXIV of Coming Forth by Day in the Underworld (commonly known as the Egyptian Book of
the Dead-Chapter LXIV)8.
As a second step, I considered the Great Step-South Wall distance (C0C-2) form three different
lengths, see figure 6, as follow:
1. Great step - King's Chamber North wall (Co C-1) = 8.4234 m
2. Great step - King's Chamber South wall (Co C-2) = 13.6595 m
3. King's Chamber North wall - South wall (C-1C-2) = 5.2361 m
Applying the Great Pyramid Dual Formula and then solving the mathematical interactions between
the three distances 8.4234 m, 13.6595 m, 5.2361 m, and the Pyramid half base (B) respectively,
provided the following three arithmetical formulas:
1. B / 13.7082 = 8.4234 m
2. B / 8.4721 = 13.6595 m
3. B / 22.1803 = 5.2361 m
Whereas (B) is the half base length of the pyramid meridian triangle in AALLLL TTHHRREEEE ccaasseess, which for
convenient reason we will writ it as B1, B2 and B3 in order to distinguish between the three cases. The
three denominators 13.7082, 8.4721 and 22.1803 are the constants of the three mathematical
interactions respectively. Therefore, the previous three formulas can be articulated as:
m
B
B
B
2361.5
6595.13
4234.8
1803.224721.87082.13
3
2
1
Hence, the three computed half base length of the Great Pyramid meridian triangle is:
7 “Pyramids and Temples of Gizeh”, Sir Flinders Petrie, W. M. London, 1883.
8 Appendix 1, The Egyptian Book LXIV of “Coming Forth by Day in the Underworld”.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
13
B1 = 13.7082 × 8.4234 = 115.4700 m
B2 = 8.4721 × 13.6595 = 115.7251 m
B3 = 22.1803 × 5.2361 = 116.1378 m
At this point, we have to recognize that each of the three calculated half base B1, B2 and B3, is only
correspond to (i.e. depend only on) one of the three distances (C-1Co), (C-2Co), and (C-2C-1)
respectively.
Comparing the difference between the three calculated half bases B1, B2 and B3 considering the
shortest half base B1 as a reference length. Will show the extraordinary accuracy or length
difference between the three computed lengths involving a distance of more than 100 m long, which
cause the hollowing effect of the Great Pyramid as follow:
If, B1 - B1 = 0.0 m
Then, B2 - B1 = 0.2551 m
B3 - B1 = 0.6678 m
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
14
The three lengths of the Great Pyramid base
Comparing the calculated three half bases B1, B2 and B3 with Davison’s hypothesis of the three base
lengths AB, AEFB, and AEbFB of the Great Pyramid of figure 7, provide:
B1 = AB / 2 Shortest
B2 = AEFB / 2 Longer
B3 = AEbFB / 2 Longest
Finally, the three calculated lengths of the Great Pyramid base according to Davidson’s assumption
respectively are:
AB = 2B1 = 2 × 115.4700 = 230.9400 m
AEFB = 2B2 = 2 × 115.7251 = 231.4502 m
AEbFB = 2B3 = 2 × 116.1378 = 232.2755 m
A B
CD
L M
NO
E F
G
H
JK
P
R
12 3
4
5
6
a
b
c
d
12
11
710
"12345.....12" is the base of the core masonry"LMNO" is the base as actually built
AEFBGHCJKDPR is the casing stone limit at the base© M. Sabet 2003
89
7. (repetitation, of figure from page 9). Illustration
of Davidson’s asumption of the Great Pyramid three
base lengths AB, AEFB and AEbFB.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
15
EEVVAALLUUAATTIIOONN OOFF TTHHEE GGRREEAATT PPYYRRAAMMIIDD CCOOMMPPUUTTEEDD RREECCOORRDDSS
Geodetic Datums
Geodetic datums define the size and shape of the earth and the origin and orientation of the
coordinate systems used to map the earth. Hundreds of different datums have been used to
frame position descriptions since the first estimates of the earth's size were made by Aristotle.
Datums have evolved from those describing a spherical earth to ellipsoidal models derived from
years of satellite measurements.
Geodetic Reference System Ellipsoid 1980 (G.R.S.’80)
The data collected by the American navigational satellites of the earth survey, better known as the
table of the Geodetic Reference System Ellipsoid 1980 (G.R.S.'80); has put an end to the various
ellipsoid systems used earlier. Moreover, it has put an end to the endless academicians argue about
the earth longitude and latitude measurements. All this approaches is due to the reliability and
accurate measurements of the G.R.S.'80 system.
According to Greenwich, the base of the Great Pyramid is centred at the intersected latitude and
longitude lines of 30° north and 31° east.
As next step, we will examine the computed accuracy of the Great Pyramid shortest base length
(AB=230.94 m) compared with the G.R.S.’80 data at (30°, 31°) and see what it means.
The proportion of 1/43,200
During my study on the form and measures between the Great Pyramid and the northern
hemisphere, I found that areas of all squires that could be created starting at the Pyramid base
moving up until the top, would squares9 all the longitudinal circles of the northern hemisphere
starting at the great circle of the equator moving up north until the northern pole on a scale of:
Great Pyramid / Northern Hemisphere = 1 / 43,200
In fact, this breakthrough combine ‘Distances’, ‘Time’ and ‘Speed’ of the earth daily rotation
reduced to the scale 1/43,200 in the Great Pyramid designed pattern. This subject is still under
going research, and in order to verify part of it is beyond the scope of this article.
Nevertheless, next, I will show an example of how the calculated base length AB (the shortest) is so
accurately calculated; or coded in the Pyramid inner distance (Co C-1) figure 6, to be equal to 7.5
second of degree latitude on the Great Circle (figure 9 appendix 2) of the Great Pyramid at 30°
north.
9 The Pyramid base squares the circle; means that: the perimeter of the Pyramid square base will equale in length to the
circumference of the circle which has a radius equal to the Pyramid height.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
16
The Great Pyramid base is 7.5 second of degree latitude at 30° north
Comparing the length of the Great Pyramid shortest base AB with the length of one second of
degree latitude of the GRS’80 table at 30° north, show an astounding precision. Comparison has
confirm that the length of the Pyramid shortest base (AB=230.9400 m) is precisely equal to 7.5
second of degree latitude at 30° north. Therefore, according to the GRS’80 table10, the length of
one-degree latitude at (30°) north is 110,852.00 m. Then:
1. GRS’80 one second of degree latitude at 30° north = 110,852.00 / 3600 m
= 30.7922 m
Considering the shortest base (AB) of the Pyramid is 7.5 second of degree latitude. Then,
2. Great Pyramid one second of degree latitude at 30° = 230.9400 / 7.5 m
= 30.7920 m
Comparing the two results show the amazing accuracy of the computed length of one second of
degree latitude coded in the Pyramid shortest base (AB=230.94 m). Such accurate length almost to
the millimetre would not be recognized or accepted before 1970 due to the many systems used.
Thanks to the data of the GRS’80 table and after all to the superior coded knowledge of the Great
Pyramid.
This previous discovery, which I made almost 16 years ago, has confirmed strongly the account of
Stecchini about the length of the land of Egypt as 7.5° latitude, as we will see next.
The length of the land of Egypt is 7.5 degree latitude
In his splendid appendix “Notes on the relation of ancient measures to the Great Pyramid”, Livio
Catullo Stecchini in Tompkins remarkable book "SSEECCRREETTSS OOFF TTHHEE GGRREEAATT PPYYRRAAMMIIDD" verified the
latitudinal length of the land of Egypt as follow:
'The length of Egypt from the most southern point to the most northern point (Behdet11 city), is 7.5
degree'.
Scale proportion of 1: 3600
Obviously by comparing the length of the Great Pyramid base ‘AB’ as 7.5 second of degree latitude,
and the Stecchini’s statement of 7.5 degree latitude for the land of Egypt length would confirm and
show the planned scale ratio between the two by the Egyptians as:
Great Pyramid shortest base ‘AB’ : north-south length of Egypt = 1 : 3600
Once again, the Great Pyramid reveals a new coded record concerning the north-south sacred length
of the land of Egypt.
10
Appendix 2. 11
Behdet city is the most northern town of Egypt, 7.5° north of the tropic, which was the capital of Egypt in the pre dynastic times.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
17
CONCLUSION
It is well known to modern scientists that the Great Pyramid of Gizeh enclose data of astronomy,
geodesy, physics, geometry, mathematics, numerology, et cetera. In fact, the Great Pyramid is a
universal library of ancient Egyptian collective records which is registered genuinely in the language
of stones by the magical attributes of numbers and geometry of the Harmonic Growth theory.
Despite of the entirely vanished layer of casing stone, the researcher has successfully calculated
the three different lengths of the Great Pyramid base. Whereas, each length were designed to
correspond to one of the three distances embodied in the distance between the Great Step and the
south wall of the King Chamber.
Indeed, these three computed lengths emphasis David Davidson’s hypothesis of the three lengths at
the Great Pyramid base due to the hollowing effect of each face. Calculation was mainly based upon
the next two explored facts by the author:
1. The dual relationship of corresponding parallels between the inner and the outer designed
lengths of the Great Pyramid architectural structure.
2. The Sabet Equation or the Dual Quadratic Formula of the Great Pyramid:
± a F0 2 ∓ bF0 S0 ∓ cS0
2 = 0
Geometrical and Math analyses of the Sabet formula have emphasized the fact that the Great
Pyramid was designed by the theory of the Harmonic Growth or the Golden Section. The key
conception of this creative theory is that; it is always growing in or out. Yet it never covers the
same pass twice, so that it does not only explain its past, but it also prophecies its future, and while
it defines what has already been happened, it leads always to a new discovery based on its past.
The composed form of ‘Sabet Equation’ or the ‘Dual Quadratic Formula of the Great Pyramid’ has in
fact doubled the talented interactivity and integrated characteristics of the Harmonic Growth
theory. This dual arithmetical tool has proven to be the key to unlock the coded treasures hidden
within this unique edifice. Because, it was certainly the tool used to code those facts which we have
explored and the many more of which we still have to detect. For remarkably enough, it seems that
the designer architect implemented his plan by designing the Great Pyramid's major features as a
set of interlocked puzzles for later investigators to recognize, solve, and thereby read the
message. When this stony puzzle would be solved and the message could be read; only then, the
architect has succeeded to deliver his message. He inscribed his perplex memo in the
unmistakable language of mathematics and geometry using universal laws as distance, time and
speed etc. He even recorded the length of the MMeettrree, the RRooyyaall CCuubbiitt and the ssiixxttiieetthh ssyysstteemm of
count, information which we still use today in our modern civilization thousands of years later.
Therefore, it would be far the better if we can regain once more the lost knowledge of the ancients
Golden Age, for these inherited treasures are the true heritage of all truth-seeking men and women
of the earth. Let us work out the divine truth of the Great Pyramid’s stony records and find the
proper way to use our knowledge, understanding and technology to explore the proper way to get
back the divine intelligence and hidden wisdom of ancient Egypt coded in THE STONES OF TRUTH.
M. Sabet
Delft-Holland
March 2004
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
18
APPENDIX 1
The Egyptian Book of “COMING FORTH BY DAY IN THE UNDERWORLD”
Invented the world’s first calendar since over 6000 years ago; the Egyptian priests considered
the appearance of the star SSeepp--DDeett (Sirius) and the beginning of the Nile flood as the start of
their calendar cycle for the New Year. Ancient Egyptians always kept their records and divine
knowledge in the form of a masterpiece building or a papyrus book. One of these papyrus which
describe the year calendar is the one known as “THE BOOK OF COMING FORTH BY DAY IN THE
UNDERWORLD”, commonly known as the Egyptian Book of the Dead-Chapter LXIV.
This book was introduced by Wallis Budge12 as: this chapter is one of the oldest of all sacred
books ever found. There are two versions of it which have been existed in ancient times.
1. A longer version named “The Book of Coming Forth by Day in the Underworld” and,
2. A shorter version called “The Book of Knowing the Book of Coming Forth by Day in a Single
Book”.
On a coffin of the XIth dynasty both versions occurred, the one immediately followed the other.
The first version ascribed it to the reign of Pharaoh SSeemm--TTii (Hesep-Ti) of the First Dynasty
(4266 BCE). While the second rubric attributed its discovery to the time of the Fourth Dynasty
Pharaoh MMeenn--kkaauu--RRââ (Mycerinus-2490-2472 BCE) builder of the Gizeh third Pyramid. I will cite
next a part from the book longer version, which says:
"I know the abysses is thy name. I work for you, O ye Spirit-four millions, six
hundred thousand, one thousand and two hundred are they-concerning the
things which are there. [I am] over their affairs working for hours and days in
setting straight the shoulders of the twelve Sah gods, and joining the hands of
their company, each to each; the sixth who is at the head of the abyss is the
hour of the defeat of the Fiends. [I] have come there in triumph".
Already known to the First Dynasty (4266 BCE), the number 4,601,200 and its derivatives seems
to be involved in many aspects and skills of the Egyptian life onward. For as we shall see soon, a
practical Golden Section number will be driven out the number 4601200 which will be the tool to
compute the following two subjects:
1. The Great Step-South wall distance.
2. The basic year of the Egyptian calendar at the six hour who are at the
head of the abyss or the New Year cycle.
12
The Egyptian Book of the Dead; Wallis Budge, E. A.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
19
Divinity of the Number 4601200
The ancient Egyptians knew various forms of the Golden Section proportion. They witnessed its
genuine existence in almost every thing they examined in their life. Nearly all traces they left
behind stands as a witness for this fact to be examined by us.
The Egyptian priests adopted and invented numerical values for each mathematical13 solution of
the different divine proportions form. In fact, their invented values do fit more the reality of the
world created around them than the theoretical or the mathematical values. As an example, we all
know that earth is not a perfect share; neither does it rotate in perfect circles around the sun.
Yet, in many cases the Egyptians employed both the invented and the theoretical numerical values
of this different Divine Proportions in their left behind work. Therefore, to obtain the practical
value of the Golden Section number invented by the Egyptians, I the number 4601200 to the
power (1/16) as follow:
Egyptian invented Golden Section number = (4601200)1/16
= 2.6087318
= 2
In the matter of fact, as we shall see soon, this invented number (2=2.6087318) is nothing but
one tenth of the distance between the edge of the Great Step and the South Wall of the King
Chamber in Egyptian Royal Cubit.
Calculation of the Great Step–South Wall distance
I considered the length of the Great Step-South Wall distance to be equal to ten times the
number (4 601 200)1/16 in Royal Cubit14 of 0.523606 m, therefore:
The distance Great Step-South Wall = 10 × (4 601 200)1/16 RC
= 26.087318 RC
= 26.087318 × 0.523606 m
= 13.659497 m
Knowing that the King's chamber breadth is 10 royal cubits (perfect number) i.e. 5.23606 m, then,
the distance between the northern wall and the great step is 16.08731874 royal cubits, i.e. 8.4234
m. Therefore, the three distances created by the dividing point (C-1) see figure 6, are:
1. King's Chamber north wall - Great Step (C-1 Co) = 16.087318 RC
= 8.4234 m
2. King's Chamber south wall - Great Step (C-2 Co) = 26.087318 RC
= 13.6595 m
13 The solution of the abc formula F2-nF-1 = 0, (whereas n = 1,2,3…n) gives a series of Golden Section numbers which
possess unique geometrical and mathematical properties, the absolute solutions are [(1.618, 0.618), (2.4142, 0.4142),
(3.3027, 0.3027)…. etc]. More details about the adopted advantages of the Golden Section for the third solution (3.3027,
0.3027) to the Golden Section meter/foot relationship see the author’s article “The Austerlitz Golden Foot, a man-made
landscape-2002”. 14 See the author article “The Golden Section Meter and Toyal Cubit of Gizeh and Orshalem”.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
20
3. King's Chamber south wall - North Wall (C-2 C-1) = 10 RC
= 5.23606 m
These are the three lengths I employed to the Great Pyramid formula to calculate the three
different lengths (AB), (AEFB) and (AEbFB) of the Great Pyramid base, according to Davidson’s
assumption as 230.9400 m, 231.4502 m and 232.2755 m respectively.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
21
APPENDIX 2
THE GEODETIC REFERENCE SYSTEM ELLIPSOID 1980
Positions on the rounded surface of the earth are defined by the universal system of latitude and
longitude. Recently, efforts to develop an accurate world geodetic system based on satellite
observations is a realized approach. The Geodetic Reference System Ellipsoid15 1980 (G.R.S.'80),
table16 2, established the length of latitude and longitude degrees of the earth's northern
hemisphere as follow:
1. The latitude degrees are measured from the equator, with positive values going north
and negative values going south.
2. The longitude degrees are measured from the Prime Meridian (Greenwich, England), with
positive values going east and negative values going west.
15
The ellipsoid has the following parameters: a = 6 378 137.000; f = 289.2572221 16
Source: Computed from the data supplied by National Geodetic Survey, Campbell, J. 'Introductory Cartography', Prentice Hall, 1984.
8. Illustration of the latitude () and longitude () positive and negative directions on the world map.
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
22
Table 4. The length of 1° intervals of selected latitudes and longitudes
Latitude
In degree
Latitude17 Longitude18
Kilometres Miles Kilometres Miles
0
5
10
15
20
110,574
110,583
110,608
110,649
110,704
68,707.3
68,712.9
68,728.5
68,753.9
68,788.1
111,319
110,899
109,639
107,551
104,647
69,170.3
68,909.3
68,126.4
66,828.0
65,024.5
25
30
35
40
45
110,773
110,852
110,941
111,035
111,132
68,831.0
68,880.1
68,935.4
68,993.8
69,054.1
100,950
96,486
91,288
85,394
78,847
62,727.3
59,953.5
56,723.6
53,061.3
48,993.1
50
55
60
65
70
111,229
111,324
111,412
111,493
111,562
69,114.3
69,173.4
69,228.0
69,278.4
69,321.3
71,696
63,994
55,800
47,176
38,187
44,549.7
39,763.9
34,672.4
29,313.7
23,728.3
75
80
85
90
111,618
111,660
111,685
111,694
69,356.1
69,382.2
69,397.7
69,403.3
28,902
19,393
9,735
0.000
17,958.8
12,050.2
6,049.0
0.000
The Earth Great Circle of the Great Pyramid
The Great Circle of the Great Pyramid is a plane passing through the Pyramid meridian and the
centre of the earth, cutting the earth surface in a great
circle as in figure 7.
The earth Small Circle of the Great Pyramid is a longitudinal
plane passing through the east-west axis of the Pyramid
base and is perpendicular to the north-south axis of the
earth (still under research).
17. Length of a degree of arc along the latitude named.
18. Length of a degree of arc centred on the longitude named.
Earth's
Center
Pole
Small Circle
M. Sabet2003
30° N
Great
Pyramid
9. The earth Great Circle (verticaly) and
the Small Circle of the Great Pyramid
(horizontaly).
STONES OF TRUTH-GIZEH 1
M. SABET-DELFT
2004
23
LITERATURE/BIBLIOGRAPHY Bauval, R. Secret Chamber, the quest for the hall of records, Century, London, 1999
Campbell, J. INTRODUCTORY CARTOGRAPHY, Prentice-Hall, 1984
Davidson, D. and, The Great Pyramid its divine message, Williams and Norgate, ltd. London, 1948 Aldersmith, H.
Edwards, I.E.S. THE PYRAMIDS OF EGYPT: Penguin, New York, 1980
Else, C. K. Geometry in Egyptian Art, U.K.: Suttons, 1953
Flinders Petrie, Kt Measures & Weights, Methuen & co. LTD, London, 1934
Flinders Petrie, W. M. Pyramids and Temples of Gizeh, Field & Tuer, London, 1883
Gaunt, Bonnie The magnificent numbers of the Great Pyramid and Stonehenge, Jackson, Michigan, 1988
Gillings, R.J. Mathematics in the time of the pharaohs, Dover publications, Inc. New York, 1972
Hayutman, Y. I. Realizing The Heavenly Jerusalem, published by the Academy of Jerusalem, 1995
Hecht, N.F.S. The Great Pyramid its geometrical basis and numerical relations in astronomy and chronology,
Covenant, 1950
Huntley, H.E. The divine proportion a study in mathematical beauty, Dover, New York, 1970
Ivimy, J. The Sphinx and the Megaliths, Abacus, Sphere Books, 1976
John Michell The New View Over Atlantis, Thames and Hudson Ltd, London, 1995
John Michell The Temple at Jerusalem: a Revelation, Gothic Image Publications, Glastonbury, England, 2000
Kanan Makita The Rock, a tale of seventh-century Jerusalem, Pantheon book, New York, 2001
Lemesuries, P. The Great Pyramid Decoded, Element, 1977
Saïd Nuseibeh, and The Dome of the Rock, Thames and Hudson Ltd. London, 1996
Oleg Grabar
Sélicourt, A. Herodotus the histories, Penguin, New York, 1987
Staniland Wake, C. The origin & significance of the Great Pyramid, Wizards bookshelf, San Diego, 1987
Theodore, A.C. The curves of life, Dover: Unabridged, 1978
Tompkins, P. Secrets of the Great Pyramid, Happer Colophon, 1978
Turnbull, H.W. The great mathematicians, New York University, 1961
Vecht, C.F. van der De stenen spreken, Den Haag, W.P. van Stockum, 1950
Waerden, B.L. van der Sience awakeing, A.W. Sijthoff, Leiden, 1975
Wallis Budge, E.A. The Book of the Dead: Routledge and Kegan Paul, 1923
Illustration credits
‘Stones of Truth – The three calculated lengths of the Great Pyramid base, M. Sabet 2004’
Figure 1 The area of each face is equal to the square of the Pyramid height; Author
Figure 2 Aerial view of the Great Pyramid showing clearly the hollowing effect at the middle of the western and
eastern faces, which was discovered accidentally by British Air Force pilot, P. Groves 1940.
Figure 3 The hollowing effect of the Great Pyramid faces exaggerated and depths of the courses magnified;
Author
Figure 4 Illustration of Davidson’s assumption of the Great Pyramid base, showing three different lengths AB,
AEFB and AEbFB to compute the solar, the sidereal and the anomalistic years; Author
Figure 5 The geometrical solutions C0 , C-1 , and C-2 of the quadratic dual formula of the great pyramid; Author
Figure 6 The Great Step-south wall distance (CoC-2) divided by the geometrical solution to (C0C-1) and (C-1C-2).;
Author
Figure 7 (repatriation, of figure from page 9); Author
Figure 8 Illustration of the latitude () and longitude () positive and negative directions on the world map;
Author
Figure 9 The earth Great Circle and Small circle of the Great Pyramid; Author
