"The Great Pyramid has lent its name as a sort of by-word for paradoxes; and, as moths to a candle, so are theorisers attracted to it. The very fact that the subject was so generally familiar, and yet so little was accurately known about it, made it the more enticing; there were plenty of descriptions from which to choose, and yet most of them were so hazy that their support could be claimed for many varying theories."
Sir Flinders Petrie
The Pyramids and Temples of Gizeh
Southern face of the Great Pyramid.
The base originally measured about 230.33m square.
The original height was 146.59m.
Location
Location: 29° 59' N 31° 09' E
Satellite images of the Egyptian Pyramids:
Click to view larger image
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The Great Pyramid (the Pyramid of Khufu, or Cheops in Greek) at Gizeh, Egypt, demonstrates the remarkable character of its placement on the face of the Earth.
The Pyramid lies in the center of gravity of the continents. It also lies in the exact center of all the land area of the world, dividing the earth's land mass into approximately equal quarters. 
The Plate XX from an original 1877 copy of
Piazzi Smyth's "Our Inheritance in the Great Pyramid".
Charles Piazzi Smyth (1819-1900) was Astronomer Royal for Scotland
and a respected Scientist.
The north-south axis (31 degrees east of Greenwich) is the longest land meridian, and the east-west axis (30 degrees north) is the longest land parallel on the globe. There is obviously only one place that these longest land-lines of the terrestrial earth can cross, and it is at the Great Pyramid! This is incredible, one of the scores of features of this mighty structure which begs for a better explanation.
Related local link:
http://www.world-mysteries.com/alignments/mpl_al2b.htm#Pyramids
Khufu Pyramid Statistics
A total of over 2,300,000 (or only 590,712)* blocks of limestone and granite were used in its construction with the average block weighing 2.5 tons and none weighing less than 2 tons. The large blocks used in the ceiling of the King's Chamber weigh as much as 9 tons.
- Construction date (Estimated): 2589 B.C..
- Construction time (Estimated): 20 years.
- Total weight (Estimated): 6.5 million tons.
- The estimated total weight of the structure is 6.5 million tons!
Original entrance of the Great Pyramid.
Massive blocks of limestone form a relieving arch over the entrance.
- The base of the pyramid covers 13 acres, 568,500 square feet and the length of each side was originally 754 feet, but is now 745 feet.
- The original height was 481 feet tall, but is now only 449 feet.
The majority of the outer casing, which was polished limestone, was removed about 600 years ago to help build cities and mosques which created a rough, worn, and step-like appearance.
* According to Socrates G. Taseos, the actual number of stones used to build the Great Pyramid is only 590,712. In his book Back in Time 3104 B.C. to the Great Pyramid- Egyptians Broke Their Backs to Build It- How the Great Pyramid Was Really Built he presents results of his computer calculations. The following is derived from the book mentioned above.
The base measurements of the Great Pyramid are: north - 755.43 ft; south -
756.08 ft; east - 755.88 ft; west - 755.77 ft. These dimensions show no two
sides are identical; however, the distance between the longest and shortest
side is only 7.8 inches.
Each side is oriented almost exactly with the four Cardinal points. The
following being the estimated errors: north side 2'28" south of west; south
side 1'57" south of west; east side 5'30" west of north; and west side 2'30"
west of north.
The four corners were almost perfect right angles: north-east 90degrees 3'
2"; north-west 89 degrees 59'58"; south-east 89 deg 56'27"; and south-west
90 deg 0'33".
When completed, it rose to a height of 481.4 ft., the top 31 feet of which
are now missing. It's four sides incline at an angle of about 51deg. 51 min.
with the ground. At its base, it covers an area of about 13.1 acres. It was
built in 201 stepped tiers, which are visible because the casing stones have
been removed. It rises to the height of a modern 40-story building.
THE BEDROCK AND CORE
The pyramid is built partly upon a solid, large, bedrock core and a platform
of limestone blocks which can be seen at the northern and eastern sides. The
builder of this pyramid was very wise to choose this site because most of
the stones, with the exception of the casing stones, some granite and basalt
stones, could be cut right on the spot and in the nearby quarry. This
practical choice made it possible to reduce considerably the time and
back-breaking labor needed to drag the stones from distant quarries across
the Nile.
The first Step of the pyramid rests on a platform of finely finished
limestone blocks. These blocks are approximately 2.5 ft x 10 ft x 10 ft..
They project beyond the outer edges of the first Step's Casing Stones an
average of 2 feet on all sides. This platform is so flat that the official
survey of the Egyptian Government found that it was less than ½ of an inch
from being level. The removal of several platform stones showed that the
bedrock had been cut and leveled to receive each individual stone, sometimes
as deep as 1 to 2 inches.
On the north side the platform stones have been laid at an irregular angle,
each socket being carefully cut to receive the next stone. One explanation
for this irregularity of stone placement is that these northern platform
stones will have greater resistance to sliding from the downward and
horizontal pressures of the pyramid's face.
The many surveys done on the pyramid proved that the Egyptians located the
sides of the pyramid along the four Cardinal Points with extreme accuracy.
Whether they used the stars, and/or the rising and setting sun, cannot be
determined. One this is certain, that whatever method they used was direct
and very simple.
Once the sand, gravel and loose rocks had been removed, down to the solid
bedrock of the plateau, the whole pyramid site was open-cast quarried into
blocks, leaving a square core for the center of the pyramid (the core is
approximately 412.7 ft square, and rises approx. 46.25 feet high). These
blocks were then stored outside a low wall; made of mortared stone that
surrounds the core (the outside dimensions of the wall are approx. 887.3
feet square). Today there still remains the foundation of this wall on the
north, south and west sides of the pyramid, at an average distance of 65
feet from the outer edge of the base casing stone.
This core gives the pyramid stability from the downward and horizontal
forces that will develop from the superimposed loads of blocks of stones
that are piled up, as the pyramid rises. Also, from the prevailing
north-west winds that exert enormous pressures on the huge areas of the
pyramid's faces, thus increasing these forces further.
Leveling of the entire pyramid site was accomplished by flooding the area
inside the wall with water, leaving just the high spots. These them were cut
down to the level of the surface of the water. Next, some of the water was
released and the high spots again were cut down to the water's surface. This
process was repeated until the entire pyramid site, between the core and the
four walls, was leveled down to the base of the pyramid's platform.
THE CASING STONES
A few of the fine limestone casing blocks remain at the base of the northern
side and show how accurately the stones were dressed and fitted together.
The core masonry, behind the casing stones, consists of large blocks of
local limestone, quarried right on the spot, built around and over the
bedrock core. The size of this core cannot be determined, since it is
completely covered by the pyramid.
The casing stones were of highly polished white limestone, which must have
been a dazzling sight. Unlike marble, which tends to become eroded with time
and weather, limestone becomes harder and more polished.
HOW MANY BLOCKS DID IT ACTUALLY TAKE TO BUILD THE GREAT PYRAMID?
Most books and encyclopedia state that there are 2.3 million blocks of stone
in the Great Pyramid of Khufu (Cheops), with no mention of method used to
figure this.
Socrates determined the size and weight of the blocks (a standard block),
and ran a Pascal Computer Program (a mathematical model of all the blocks of
stone needed; written by the author to optimize the sizes and weights of the
stones) to come up with the real number of blocks used. Since the volume of
passageways and internal chambers are very small compared to the high volume
of the pyramid, they are ignored at this time, just as though the pyramid
was built of solid stone blocks with mortared joints.
THE SIZE OF THE BLOCKS
The size of the blocks are based on a chance discovery in 1837 by Howard
Vyse. He found two of the original side casing blocks at the base of the
pyramid, 5 ft x 8 ft x 12 ft, with an angle of 51 degrees, 51 minutes cut on
one of the 12 ft. sides. Each of these stones weighed (5 x 8 x 12)/2000 =
39.9 tons before the face angle was cut. These originally were used for the
side casing stones of Step No. 1, in the Pascal computer program. The sizes
of all the other blocks were scaled from these two original blocks of the
remaining Steps 2 to 201.
THE GREAT PYRAMID'S DIMENSIONS AND THEIR LAYOUT
One acre = 43,560 sq. ft, or 208.71 feet on a side.
For the pyramid's base, length = width = (square root of 13.097144 acres) x
208.71 feet = 755.321 feet. Or 755.321 x 12 = 9063.85 inches.
Height = (755.321 x tangent 51deg 51 min)/2 = 480.783 feet. Or 480.783 x 12
= 5769.403 inches.
For the cap stone base: length = width = (32.18 x 2)/tangent 51deg 51 min =
50.55 inches.
The average size of a pyramid stone = (5 x 8 x 12)
The average side measurement, at the base = 759.3 ft.
The height used was 201 steps high, or 480 feet. (This is minus the height
of the Capstone, which was one piece in itself.
The number reached by the Pascal computer program was 603,728 blocks used.
The solid core takes up the space of 13,016 stones.
So, the actual number of stones used to build the Great Pyramid is 603,728 -
13,016 = 590,712.
This figure is (2,300,000 - 590,712) = 1,709,288 blocks less than the often
published 2.3 million value.
NUMBER OF VARIOUS BLOCKS OF STONE USED TO BUILD THE GREAT PYRAMID
Number of platform blocks used (2.5 ft x 10 ft square), equals (759.3 x
759.3(pyramid base)) - (412.7 x 412.7(core base))/(10 x 10(platform block
base)) = 4,062.
Number of CORNER Casing stones where the pyramid faces meet equals 201 steps
x 4 sides = 804.
Number of side casing stones equals ((244 x 127) + 8,953) = 39,941.
Due to Bedrock Core, in the center of Step 1 through 10, the total number of
blocks needed is reduced by 13,016.
THE NUMBER OF ALL BLOCKS BEHIND THE CASING STONES EQUALS
(590,712 - 804 - 39,941) = 549,967.
PLACING THE BLOCKS
The average number of blocks that have to be placed each day equals (590,712
blocks)/(20years x 364.25 days) = 81 blocks per day.
If 10 crews of 300 men work on each of the four sides of the pyramid, then
the totals of 40 crews and 12,000 men will be needed. Each of the crews will
be responsible to place 81/40 = 2 blocks per day.
The workload passes through three phases of decreasing difficulty, which are
determined by the weights of the heaviest blocks:
Steps 1 through 21 (60.59 to 27.24 tons)
Steps 22 through 136 (17.66 to 6.44 tons)
Steps 127 through 201 (3.05 to 2.63 tons)
As the weight of the blocks decrease, Step to Step, the sizes of the drag
crews will decrease. However, when this happens, the number of blocks needed
to be dragged each day can be reduced because one large block can be dragged
and cut into several smaller blocks that are needed.
As the pyramid rises there is less space for the crews to work in and fewer
block to be placed. In other words, the number of workers that will be
needed depends on three factors of: weight of blocks, number of blocks to be
placed, and the working space available.
© 1990 by Socrates Taseos
Related Books on the Ancient Egypt
Geometry of the Great Pyramid
DIMENSIONS of Great Pyramidby morphvs The following article is Copyright © 2001-2003 aiwaz.net_institute.
If the calculations concerning the royal cubit are correct the main dimensions of the pyramid should also prove that. The approximate dimensions of the pyramid are calculated by Petrie according to the remains of the sockets in the ground for the casing stones whose remains are still at the top of the pyramid, and the angle 51° 52' ± 2' of the slopes. The base of 9069 inches is approximately 440 royal cubits (the difference is 9 inches which is not a remarkable difference if we consider the whole dimension and consider that the employed data represent only an estimation of the real values) whereas the calculated height, 5776 inches, is precisely 280 royal cubits. The relation 440:280 can be reduced to 11:7, which gives an approximation of the half value of Pi.
The engagement of Pi value in the main dimensions suggests also a very accurate angle of 51° 52' ± 2' of the slopes which expresses the value of Pi. Another coincidence is the relation between the height of the pyramid's triangle in relation to a half of the side of the pyramid, since it appears to be the Golden Section, or the specific ratio ruling this set of proportions, F = (sqr(5)+1)/2 = 1.618 = 356:220. This ratio, 356:220 = 89:55 is also contained in the first of Fibonacci Series: 1 2 3 5 8 13 21 34 55 89 144 ... A single composition contains two apparently contradicting irrational numbers P and F, without disrupting each other. This appears to be completely opposed to the classical architectural canon which postulates that in 'good' composition no two different geometrical systems of proportions may be mixed in order to maintain the purity of design. But analysis of other architectural and artistic forms suggested that the greatest masters skillfully juggled the proportional canons without losing the coherent system, for they knew that these systems can be interconnected if the path that links them is found. That is obvious In the case of the Great Pyramid where two different principles are interweaved without interference ruling different angles of the composition, which is most importantly a most simple one, namely 11:7, a most simple ratio obviously signifying such infinite mysteries as the value of P and most 'natural' value of F. In spite of common miss-understanding of architectural composition, the most mysterious and praised compositions are very simple but not devoid of anthropomorphic appeal, since everything is made out of human proportions, just like Vitruvius describing the rations of the human body, very simple and very clean. The numbers 7 and in 11 are successive factors in the second of Fibonacci progressions that approximate geometry of the pentagram: 1 3 4 7 11 18 29 47 76 123 ... The summary of the selected main mean dimensions is:
The main source of all kinds of delusions and speculations about our mythical past for the western man comes of course from Plato. With the myth of Atlantis he planted the necessary seed of mythical Eden, a culture of high intelligence that lived before the known history. If Plato received any wisdom from the ancient Egypt it could perhaps be traced in the canon of numbers that is so latently present throughout his work, but never on the surface. This canon seems to appear in the descriptions of his fantastic cities where everything is most carefully calculated and proportioned. The topic of Plato's Laws is the description of the ideal state called Magnesia which is entirely composed out of the mysterious number 5,040. The distance* when Earth is closest to Sun (perihelion) is 147x106 km, which is translated into royal cubits 280x109, hinting at the height of the Great pyramid, The above article comes from aiwaz.net_institute - Great Pyramid and Giza plateau * Related links: Astronomic & Cosmographic Data, Nasa site with planetary data Do not miss this web site: aiwaz.net_institute - Great Pyramid and Giza plateau |
The Golden Ratio & Squaring the Circle in the Great Pyramid
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less. [Euclid]
The extreme and mean ratio is also known as the golden ratio.
If the smaller part = 1, and larger part = G, the golden ratio requires that
G is equal approximately 1.6180
Does the Great Pyramid contain the Golden Ratio?
Assuming that the height of the GP = 146.515 m, and base = 230.363 m, and using simple math we find that half of the base is 115.182 m and the "slant height" is 186.369 m
Dividing the "slant height" (186.369m) by "half base" (115.182m) gives = 1.6180, which is practically equal to the golden ration!
The earth/moon relationship is the only one in our solar system that contains this unique golden section ratio that "squares the circle". Along with this is the phenomenon that the moon and the sun appear to be the same size, most clearly noticed during an eclipse. This too is true only from earth's vantage point…No other planet/moon relationship in our solar system can make this claim.
Although the problem of squaring the circle was proven mathematically impossible in the 19th century (as pi, being irrational, cannot be exactly measured), the Earth, the moon, and the Great Pyramid, are all coming about as close as you can get to the solution!
If the base of the Great Pyramid is equated with the diameter of the earth, then the radius of the moon can be generated by subtracting the radius of the earth from the height of the pyramid (see the picture below).
Click here to view larger picture.
Also the square (in orange), with the side equal to the radius of the Earth, and the circle (in blue), with radius equal to the radius of the Earth plus the radius of the moon, are very nearly equal in perimeters:
Orange Square Perimeter = 2+2+2+2=8
Blue Circle Circumference = 2*pi*1.273=8
Note:
Earth, Radius, Mean = 6,370,973.27862 m *
Moon, Radius, Mean = 1,738,000 m.*
Moon Radius divided by Earth Radius = 0.2728 *
* Source: Astronomic and Cosmographic Data
Let's re-phrase the above arguments **
In the diagram above, the big triangle is the same proportion and angle of the Great Pyramid, with its base angles at 51 degrees 51 minutes. If you bisect this triangle and assign a value of 1 to each base, then the hypotenuse (the side opposite the right angle) equals phi (1.618..) and the perpendicular side equals the square root of phi. And that’s not all. A circle is drawn with it’s centre and diameter the same as the base of the large triangle. This represents the circumference of the earth. A square is then drawn to touch the outside of the earth circle. A second circle is then drawn around the first one, with its circumference equal to the perimeter of the square. (The squaring of the circle.) This new circle will actually pass exactly through the apex of the pyramid. And now the “wow”: A circle drawn with its centre at the apex of the pyramid and its radius just long enough to touch the earth circle, will have the circumference of the moon! Neat, huh! And the small triangle formed by the moon and the earth square will be a perfect 345 triangle (which doesn’t seem to mean much.)
** Source: http://geometry.wholesomebalance.com/Sacred_Geometry_2.html#Phi
Was the golden ratio intentionally built into the Great Pyramid of Cheops?
Why would anyone intentionally build the golden ratio into a pyramid, or other structure? What was the significance of to the Egyptians? And did the ancient Egyptians intentionally design the Great Pyramid to square the circle?
The answer to these questions is uncertain since designing the Great Pyramid according to the simple rules explained by the graphic below would give the pyramid automatically (by coincidence? ) all its "magic" qualities.
The height of the Great Pyramid times 2π exactly equals the perimeter of the pyramid. This proportions result from elegant design of the pyramid with the height equal two diameters of a circle and the base equal to the circumference of the circle. Click here or on the image below to see larger picture.
For the angle of the Great Pyramid, any theory of the base, combined with any theory of the height, yields a theoretic angle; but the angles actually proposed are the following** :
| Angle of casing measured | 51º 52' ± 2' (51.867) 51º 40' 16.2" |
** Page 184, The Pyramids and Temples of Gizeh
by Sir W.M.Flinders Petrie 1883
Comparing the Great Pyramid with the Pyramid of the Sun in Teotihuacan
The Pyramid of the Sun and the Great Pyramid of Egypt are almost or very nearly equal to one another in base perimeter. The Pyramid of the Sun is "almost" half the height of the Great Pyramid. There is a slight difference. The Great Pyramid is 1.03 - times larger than the base of the Pyramid of the Sun. Conversely, the base of the Pyramid of the Sun is 97% of the Great Pyramid's base.
The ratio of the base perimeter to the height:
| Great Pyramid | Pyramid of the Sun |
| 6.2800001... : 1 (deviates by 0.05 % from the 6.2831853 value for 2 x pi) | 12.560171... : 1 (deviates by 0.05 % from the 12.566371 value for 4 x pi) |
The Great Pyramid - Metrological Standard
The Great Pyramid is generally regarded as a tomb and as grandiose memorial to the pharaoh who commissioned it. The opposing view is that of the pyramid being the culminating achievement of those who practised an advanced science in prehistory.
The Great Pyramid is a repository of universal standards, it is a model of the earth against which any standard could be confirmed and corrected if necessary.
It is exactly the imperishable standard, which the French had sought to create by the devising of the metre, but infinitely more practical and intelligent.
From classical times, the Great pyramid has always been acknowledged as having mathematical, metrological and geodetic functions. But ancient Greek and Roman writers were further removed in time from the designers of the Great Pyramid than they are from us. They had merely inherited fragments of a much older cosmology; the science in which it was founded having long since disappeared.
Read More: http://www.secretacademy.com/pages/greatpyramid.htm
Related Links:
- A Comparative Geometric Analysis of the Heights and Bases of the Great Pyramid of Khufu and the Pyramid of the Sun at Teotihuacan
- http://www.secretacademy.com/pages/greatpyramid.htm
- A Brief Introduction to Ancient Metrology
- The Golden Ratio & Squaring the Circle in the Great Pyramid
- Mid-Atlantic Geomancy - Sacred Geometry
-
http://members.optushome.com.au/fmetrol/main/isopsephia.html#code
- Greek Isopsephia
- aiwaz.net_institute - Great Pyramid and Giza plateau
- More Related Links
The Following articles are © 2000 by Larry Orcutt, Catchpenny Mysteries
Reprinted with permission
The Concave Faces of the Great Pyramid
Aerial photo by Groves, 1940 (detail).
In his book The Egyptian Pyramids: A Comprehensive, Illustrated Reference, J.P. Lepre wrote:
One very unusual feature of the Great Pyramid is a concavity of the core that makes the monument an eight-sided figure, rather than four-sided like every other Egyptian pyramid. That is to say, that its four sides are hollowed in or indented along their central lines, from base to peak. This concavity divides each of the apparent four sides in half, creating a very special and unusual eight-sided pyramid; and it is executed to such an extraordinary degree of precision as to enter the realm of the uncanny. For, viewed from any ground position or distance, this concavity is quite invisible to the naked eye. The hollowing-in can be noticed only from the air, and only at certain times of the day. This explains why virtually every available photograph of the Great Pyramid does not show the hollowing-in phenomenon, and why the concavity was never discovered until the age of aviation. It was discovered quite by accident in 1940, when a British Air Force pilot, P. Groves, was flying over the pyramid. He happened to notice the concavity and captured it in the now-famous photograph. [p. 65]
This strange feature was not first observed in 1940. It was illustrated in La Description de l'Egypte in the late 1700's (Volume V, pl. 8). Flinders Petrie noticed a hollowing in the core masonry in the center of each face and wrote that he "continually observed that the courses of the core had dips of as much as ½° to 1°" (The Pyramids and Temples of Gizeh, 1883, p. 421). Though it is apparently more easily observed from the air, the concavity is measurable and is visible from the ground under favorable lighting conditions.
Ikonos satellite image of the Great Pyramid.
Click to view larger image.
I.E.S. Edwards wrote, "In the Great Pyramid the packing-blocks were laid in such a way that they sloped slightly inwards towards the centre of each course, with a result that a noticeable depression runs down the middle of each face -- a peculiarity shared, as far as is known, by no other pyramid" (The Pyramids of Egypt, 1975, p. 207). Maragioglio and Rinaldi described a similar concavity on the pyramid of Menkaure, the third pyramid at Giza. Miroslav Verner wrote that the faces of the Red Pyramid at Dahshur are also "slightly concave."
Diagram of the concavity (not to scale).
What was the purpose for concave Great Pyramid sides? Maragioglio and Rinaldi felt this feature would help bond the casing to the core. Verner agreed: "As in the case of the earlier Red Pyramid, the slightly concave walls were intended to increase the stability of the pyramid's mantle [i.e. casing stones]" (The Pyramids, 2001, p. 195). Martin Isler outlined the various theories in his article "Concerning the Concave Faces on the Great Pyramid" (Journal of the American Research Center in Egypt, 20:1983, pp. 27-32):
- To give a curved form to the nucleus in order to prevent the faces from sliding.
- The casing block in the center would be larger and would serve more suitably as a guide for other blocks in the same course.
- To better bond the nucleus to the casing.
- For aesthetic reasons, as concave faces would make the structure more pleasing to the eye.
- When the casing stones were later removed, they were tumbled down the faces, and thereby wore down the center of the pyramids more than the edges.
- Natural erosion of wind-swept sand had a greater effect on the center.
Isler dismisses the first four reasons based on the idea that "what is proposed for the first pyramid should hold true for the others." He also dismisses the last two because they would not "dip the courses," but rather have simply "worn away the surface of the stone." Adding another category to the list above, "a result of imperfect building method," he proceeds to theorize that the concavity was an artifact of a compounding error in building technique (specifically, a sag in the mason's line). One is tempted to reject this theory based on Isler's own reasoning: "what is proposed for the first pyramid should hold true for the others."
The concavity has prompted more improbable theories, usually in support of some larger agenda. David Davidson (cited by Peter Tompkins in Secrets of the Great Pyramid, pp. 108-114) defended the discredited Piazzi Smyth by attempting to demonstrate that if measurements included the hollowing, they would provide three base measurements that describe the three lengths of the year: solar, sidereal, and "anomalistic." (These lines, on the diagram below, would be AB, AEFB, and AMB.) What Davidson is assuming is that the concavity, present today in the core structure of the pyramid, would extend to the finished cased surface. There is no evidence for this; indeed the extant casing is perfectly flat. Maragioglio and Rinaldi observed that the granite casing of Menkaure's pyramid was flat, but above the granite the packing-blocks formed a concavity in the center of each face. The evidence indicates that the concavity is a functional feature of the core structure that was hidden from sight when the casing stones were applied.
Three proposed "baselines" of the Great Pyramid (not to scale).
John Williams, author of Williams' Hydraulic Theory to Cheops' Pyramid wrote that "the only advantage that I can see - and it is a great one - for having a concave face on a structure is to contain extremely high internal pressures - the type of pressures that would result from using a hydraulic method of my description. Think of this in terms of an egg shell, arch or gabling." This explanation is also voiced by other purveyors of the "pump-theory" such as Edward J. Kunkel (author of The Pharaoh's Pump, 1962) and Richard Noone (author of 5/5/2000: Ice: The Ultimate Disaster, 1982). Unfortunately, they fail to understand how an arch or load-bearing gable works. A supporting arch is designed to convert the downward force, or weight, of a structure to an outward force, which in turn is transferred to a buttress, a pier, or an abutment. An arch simply redirects the force; it does not make it vanish. If the sides of the Great Pyramid were designed as arches, then those arches would serve to direct the load into thin air. It doesn't make sense. The eggshell analogy is yet less applicable because the pyramid is not egg-shaped. Like the arch, the egg is strong because it transfers load pressure, in this case into vertical as well as horizontal forces that are distributed more evenly along the structure of the egg due to its shape.
Kunkel likened each pyramid face to a dam. He claimed that each side bends inward against the pressure of the water inside the pyramid just as a dam (Hoover Dam for example) bends towards the force of the water it holds back. An arch dam employs the same structural principles as the arch (described above). The dam curves towards the hydrostatic pressure from the water behind it, which in turn is distributed horizontally to abutments on the side walls against which the dam is built. Again, the pyramid lacks such abutments.
In Ancient Egyptian Construction and Architecture, Clarke and Englebach wrote:
Most pyramids have individual peculiarities which are as yet difficult to explain. For instance, in the Great Pyramid, as possibly in certain others, a large depression in the packing-blocks runs down the middle of each face, implying a line of extra-thick facing there. Though there is no special difficulty in arranging the blocks of a course in such a manner that they increase in size at the middle, there is no satisfactory explanation of the feature any more than there is of the 'girdle-blocks' [in the Great Pyramid's ascending passage] already discussed. [p. 128]
The purpose for the concavity of the Great Pyramids remains a mystery and no satisfactory explanation for this feature has been offered. The indentation is so slight that any practical function is difficult to imagine.
© 2000 by Larry Orcutt, Catchpenny Mysteries, Reprinted with permission
The Great Pyramid's "Air Shafts"
While shafts in the King's Chamber had been described as early as 1610, the shafts in the Queen's Chamber were not discovered until 1872. In that year, Waynman Dixon and his friend Dr. Grant found a crack in the south wall of the Queen's Chamber. After pushing a long wire into the crack, indicating that a void was behind it, Dixon hired a carpenter named Bill Grundy to cut through the wall. A rectangular channel, 8.6 inches wide and 8 inches high, was found leading 7 feet into the pyramid before turning upward at about a 32º angle. With the two similar shafts of the King's Chamber in mind, Dixon measured a like position on the north wall, and Grundy chiseled away and, as expected, found the opening of a similar channel. The men lit fires inside the shafts in an attempt to find where they led. The smoke stagnated in the northern shaft but disappeared into the southern shaft. No smoke was seen to exit the pyramid on the outside. Three artifacts were discovered inside the shafts: a small bronze grapnel hook, a bit of cedar-like wood, and a "grey-granite, or green-stone" ball weighing 8.325 grains thought to be an Egyptian "mina" weight ball.
Shafts and passages of the Great Pyramid at Giza.
The Shafts of the Queen's Chamber Described
The openings of both shafts are located at the same level in the chamber, at the joint at the top of the second course of granite wall-stone; the ceilings of the shafts are level with the joint.
The northern shaft runs horizontally for just over six feet (76"), then turns upward at a mean angle of 37º 28'. The shaft terminates about 20 feet short of the outside of the pyramid. The total length of the northern shaft is about 240 feet and rises at an angle of 38º for the majority of its length.
The southern shaft also runs horizontally for just over six feet (80"), then turns upward at a mean angle of 38º 28'. The total length of the southern shaft is about 250 feet and, as its northern counterpart, ascends at an angle of 38º for the majority of its length and comes to an end about 20 feet short of the outside of the pyramid.
The Shafts of the King's Chamber Described
The openings of both shafts are located at roughly the same level in the chamber, at the joint at the top of the first course of granite wall-stone. The northern opening is slightly lower, its ceiling being level with the joint, while the floor of the southern opening is roughly level with the joint.
The northern shaft is rectangular, about 7 inches wide by 5 inches high, a shape it maintains throughout its length. The shaft begins on the horizontal for about 6 feet then takes a series of four bends. While maintaining its general upward angle, it shifts first to the north-northwest then back to north, then to north-northeast, and finally back to true north. It has been speculated by some that this unexplained semicircular diversion might have been necessary to avoid some heretofore undiscovered feature of the pyramid. The total length of the northern shaft is about 235 feet and rises at an angle of 31º (with a variation of between 30º 43' and 32º 4') for the majority of its length.
Though the first eight feet of the northern shaft is intact, the next thirty or so feet have been excavated by treasure seekers, presumably following the direction of the shaft in search of treasure. The breach to the shaft was made in the west wall of the short passage leading from the antechamber to the King's Chamber. A modern iron grate today guards the mouth of this breach.
The southern shaft is different in appearance. Its mouth is larger, about 18" wide by 24" high. The dimensions are reduced to about 12" by 18" within a few feet, and then narrows yet more to about 8" by 12". The shape is not rectangular, as is the northern shaft, but has a dome shape where it enters the chamber, with a narrow floor, the angle of the walls being slightly obtuse, and a dome-shaped ceiling. The shaft is horizontal and true south for about 6 feet. At the first bend, its shape changes to an oval, and continues thusly for about 8 feet. Its orientation also changes slightly from true south to south-southwest. At the second bend its shape changes yet again to a rectangle, with a height greater than its width. It retains this shape for the 160 feet to the outside of the pyramid where it emerges at the 101st course of stone. It also changes directions once again at the second bend to a more severe south-southwest diversion. The total length of the southern shaft is about 175 feet and ascends at an angle of 45º (with a variation of between 44º 26' and 45º 30') for the majority of its length.
The Function of the Shafts
When Sandys described the Great Pyramid in 1610, he wrote of the shafts:
In the walls, on each side of the upper room, there are two holes, one opposite to another, their ends not discernable, nor big enough to be crept into -- sooty within, and made, as they say, by a flame of fire which darted through it.Greaves also wrote of the King's Chamber shafts in 1638. Considering the presence of the lampblack inside, he concluded that the shafts had been intended as receptacles for an "eternal lamp." In 1692, M. Maillet wrote that the shafts served as means of communication for those who were buried alive with the dead king. Not only did the shafts provide air, he reasoned, but they also provides a passage for food which was placed in boxes and pulled through by rope.
By the 20th century, the shafts were presumed to have been designed to provide ventilation. That view has slowly been changing, however. I.E.S. Edwards wrote, "The object of these shafts is not known with certainty; they may have been designed for the ventilation of the chamber or for some religious purpose which is still open to conjecture." (The Pyramids of Egypt, 1961, p. 126.) Ahmed Fakhry wrote, "They are usually referred to as 'air channels,' but most Egyptologists believe that they had a religious significance related to the soul of the king." (The Pyramids, 1969, p. 118.) More recently, Mark Lehner wrote:
A symbolic function should also be attributed to the so-called "air-shafts," which had nothing to do with conducting air. No other pyramid contains chambers and passages so high in the body of masonry as Khufu's and so the builders provided the King's Chamber with small model passages to allow the king's spirit to ascend to the stars. (The Complete Pyramids, 1997, p. 114)
There are many reasons why it is not likely that the shafts were meant for ventilation. The complex angles of the shafts necessitated the piercing of many courses of stone, a daunting logistical challenge during design and construction. Horizontal shafts would have been much easier to build: shafts carved through a single course of stone. One might well wonder why ventilation would be needed at all! No other known pyramid builder made such provisions; even workers in rock-cut tombs managed on the air provided solely by the entrance passage. When the bulk of work on the King's Chamber was being done, ambient air was plentiful as the ceiling had not yet been put in place. The chamber was finished as the superstructure rose.
There are also, however, reasons why it is not likely that the shafts were meant to serve as "launching ramps" for the king's ka. When, in 1964, Alexander Badawy and Virginia Trimble determined that the shafts are "aimed" at certain "imperishable" circumpolar stars and at the constellation of Orion, the function of the shafts as cultic features seemed certain. But the ka did not require a physical means of egress from a tomb -- false doors served this purpose quite nicely both before and after Khufu's reign. The passage that ascends to the entrance of the pyramid is also directed at the circumpolar stars in the manner of previous pyramids. The northern shafts for such a use would have been a needless and bothersome redundancy, although admittedly the Egyptians were not adverse to redundancies.
That fact that no other pyramid in Egypt is known to posses similar shafts as those of the Great Pyramid is problematic. If the shafts were so important for either ventilation or as passages for the king's ka, then why were they omitted in other funerary structures? It is obvious that the builders of Khufu's pyramid went to a jolly lot of trouble to incorporate the shafts into the design of the pyramid, but the true reason why still remains a mystery.
© 2000 by Larry Orcutt, Catchpenny Mysteries, Reprinted with permission
Shafts Related Links
Find more about the SHAFTS
from the The UPUAUT Project web site (by Rudolf Gantenbrink).
With a few minor exceptions, the four so-called "air shafts" of the Cheops Pyramid were constructed in accordance with one unvarying system. The shaft roof and both walls were cut from one block to form something like a stone canal. The floor was provided by a second block, effectively sealing the shaft from below. Thus, the joins connecting the upper blocks normally ran perpendicular to the floor of the shaft.
A link to a free 3D VRML Model of the Great Pyramid:
http://www-vrl.umich.edu/project/pyramid/index.html
One can go through all the chambers, passageways, etc. as well as make it transparent and move around the internal mass of the pyramid so as to view the internal chambers from the outside, and from any angle. Pretty well done, and a great visualization tool.
Get a free plug-in viewer here: http://www.parallelgraphics.com/products/cortona
More geometric Analysis of the Great Pyramid of Khufu:
- aiwaz.net_institute - Great Pyramid and Giza plateau
GREAT PYRAMID: Position of King's Chamber, Queen's Chamber, Subterranean Chamber; SECOND PYRAMID: Dimensions of Pyramid, Great Chamber, Coffer, Lower Chamber; THIRD PYRAMID: Dimensions of Pyramid, Chambers,MATHESIS of Giza Plateau - http://www.ronaldbirdsall.com/gizeh/petrie/index.htm
- A download link to the e-book "The Pyramids and Temples of Gizeh," by Sir W. M. Flinders Petrie 1883. This PDF file was produced by Graham Oaten of Melbourne, Australia.
Related links: - http://www.ronaldbirdsall.com/gizeh/index.htm
- Some believe that the pyramids were laid out in the pattern of the stars in the constellation Orion.
- The Great Pyramid of Khufu and the Pyramid of the Sun at Teotihuacan - A Comparative Geometric Analysis (http://www.nexusjournal.com/Reynolds.html).
Where was Khufu buried?
The question remaining to the many who have arrived by one route or another at the conclusion that he was not buried in his pyramid.
No tomb has yet been found at Giza which could have been his. At one time the idea was circulated (it is in Edgar's Great Pyramid) that the tomb near to the Sphinx, called 'Campbell's Tomb', had been that of Khufu; but this tomb is now known to be of a very much later date. Taking the procedure adopted with Hetep-heres, one can assume that Khufu would probably have chosen a position within the boundary of his royal cemetery, which limits are clearly defined, but this area has been almost entirely excavated down to the rock. The possibilities lie in the 'almost '. There is, for instance, a pre-Khufu quarry alongside and beneath his causeway, which has been filled in with large blocks of limestone and gypsum. This was done presumably to give a level floor for Khufu's causeway, which crosses it, and the filled quarry lies within a few yards of the tomb of Hetep-heres. The clearing of this would be a difficult, laborious, and expensive task; but it cannot be said that there is nothing there but a filled quarry until the quarry has been emptied.
The area of the pyramid-temple has also remained unexcavated so far, though there appears to be little left beyond the basalt floor, across a part of which thousands of tourists trek yearly to the Sphinx, and perhaps the lowest courses or other traces of some of the walls There seem to be no other possibilities so far as we know at present. That there was a problem connected with Khufu's place of burial was known in later Egyptian times, when the fact that the Great Pyramid was his work must have still been well known; and the question was then put into writing as to who knew the places of burial of Im-hetep, Seneferu and Khufu, as though it were an oft-repeated query.
Edgar Cayce - Great Pyramid and Sphinx Reading from 1932
READING 5748-6. This Reading given by Edgar Cayce July 1st 1932.
1. EC: Much has been written respecting that represented in the Great Pyramid, and the record that may be read by those who would seek to know more concerning the relationships that have existed, that may exist, that do exist, between those of the Creative Forces that are manifest in the material world. As indicated, there were periods when a much closer relationship existed, or rather should it be said, there was a much better understanding OF the relationship that EXISTS between the creature and the Creator.
2. In those conditions that are signified in the way through the pyramid, as of periods through which the world has passed and is passing, as related to the religious or the spiritual experiences of man - the period of the present is represented by the low passage or depression showing a downward tendency, as indicated by the variations in the character of stone used. This might be termed in the present as the Cruciatarian Age, or that in which preparations are being made for the beginning of a new sub-race, or a change, which - as indicated from the astronomical or numerical conditions - dates from the latter portion or middle portion of the present fall [1932]. In October there will be a period in which the benevolent influences of Jupiter and Uranus will be stronger, which - from an astrological viewpoint - will bring a greater interest in occult or mystic influences.
3. At the correct time accurate imaginary lines can be drawn from the opening of the great Pyramid to the second star in the Great Dipper, called Polaris or the North Star. This indicates it is the system toward which the soul takes it flight after having completed its sojourn through this solar system. In October there will be seen the first variation in the position of the polar star in relation to the lines from the Great Pyramid. The dipper is gradually changing, and when this change becomes noticeable - as might be calculated from the Pyramid - there will be the beginning of the change in the races. There will come a greater influx of souls from the Atlantean, Lemurian, La, Ur or Da civilizations. These conditions are indicated in this turn in the journey through the pyramid. 4. How was this begun? Who was given that this should be a record of man's experiences in this root race? for that is the period covered by the prophecies in the pyramid. This was given to Ra and Hermes in that period during the reign of Araaraart when there were many who sought to bring to man a better understanding of the close relationship between the Creative Forces and that created, between man and man, and man and his Maker.
5. Only those who have been called may truly understand. Who then has been called? Whosoever will make himself a channel may be raised to that of a blessing that is all that entity-body is able to comprehend. Who, having his whole measure full, would desire more does so to his own undoing.
6. (Q) What are the correct interpretations of the indications in the Great Pyramid regarding the time when the present depression will end?
(A) The changes as indicated and outlined are for the latter part of the present year [1932]. As far as depression is concerned, this is not - as in the minds of many - because fear has arisen, but rather that, when fear has arisen in the hearts of the created, SIN lieth at the door. Then, the change will occur - or that seeking will make the definite change - in the latter portion of the present year. Not that times financially will be better, but the minds of the people will be fitted to the conditions better.
7. (Q) What was the date of the actual beginning and ending of the construction of the Great Pyramid?
(A) Was one hundred years in construction. Begun and completed in the period of Araaraart's time, with Hermes and Ra.
8. (Q) What was the date B.C. of that period?
(A) 10,490 to 10,390 before the Prince entered into Egypt.
9. (Q) What definite details are indicated as to what will happen after we enter the period of the King's Chamber?
(A) When the bridegroom is at hand, all do rejoice. When we enter that understanding of being in the King's presence, with that of the mental seeking, the joy, the buoyancy, the new understanding, the new life, through the period.
10. (Q) What is the significance of the empty sarcophagus?
(A) That there will be no more death. Don't misunderstand or misinterpret! but the INTERPRETATION of death will be made plain.
11. (Q) If the Armageddon is foretold in the Great Pyramid, please give a description of it and the date of its beginning and ending.
(A) Not in what is left there. It will be as a thousand years, with the fighting in the air, and - as has been - between those returning to and those leaving the earth.
12. (Q) What will be the type and extent of the upheaval in '36?
(A) The wars, the upheavals in the interior of the earth, and the shifting of same by the differentiation in the axis as respecting the positions from the Polaris center.
13. (Q) Is there not a verse of scripture in Isaiah mentioning the rock on which the great pyramid is builded?
(A) Not as we find; rather the rock on which John VIEWED the New Jerusalem - that is, as of the entering in the King's Chamber in the Pyramid.
14. (Q) What is the date, as recorded by the Pyramid, of entering in the King's Chamber?
(A) '38 to '58.
15. (Q) If the Passion of Jesus is recorded in the Great Pyramid, please give the date according to our present system of recording time?
(A) This has already been presented in a fair and equitable manner through those students of same, and these descriptions have been presented as to their authenticity.
16. (Q) How was this particular Great Pyramid of Gizeh built?
(A) By the use of those forces in nature as make for iron to swim. Stone floats in the air in the same manner. This will be discovered in '58.
17. (Q) What is the significance of the character of the figure of the Sphinx, mentioned above?
(A) In this particular period of Araaraart and of the priest (that began those understandings - and passed through those of the hell in the misinterpretation of same), there was even then the seeking through those channels that are today called archaeological research.
In those periods when the first change had come in the position of the land, there had been an egress of peoples - or THINGS, as would be called today - from the Atlantean land, when the Nile (of Nole, then) emptied into what is now the Atlantic Ocean, on the Congo end of the country. What is now as the Sahara was a fertile land, a city that was builded in the edge of the land, a city of those that worshipped the sun - for the use of its rays were used for supplying from the elements that which is required in the present to be grown through a season; or the abilities to use both those of introgression and retrogression - and mostly retrograded, as we are in the present.
The beginnings of these mounds were as an interpretation of that which was crustating in the land. (See, most of the people had tails then!) In those beginnings these were left. When there was the entrance of Arart and Araaraart, they begin to build upon those mounds which were discovered through research. With the storehouse, or record house (where the records are still to be uncovered), there is a chamber or passage from the right forepaw to this entrance of the record chamber, or record tomb. This may not be entered without an understanding, for those that were left as guards may NOT be passed until after a period of their regeneration in the Mount, or the fifth root race begins. In the building of the pyramid, and that which is now called the Mystery of Mysteries [the Sphinx], this was intended to be a MEMORIAL - as would be termed today - to that counsellor who ruled or governed, or who acted in the capacity of the director in the MATERIAL things in the land.
With the return of the priest (as it had been stopped), this was later - by Isis, the queen, or the daughter of Ra - turned so as to present to those peoples in that land the relationships of man and the animal or carnal world with those changes that fade or fall away in their various effect. These may be seen in a different manner presented in many of the various sphinxes, as called, in other portions of the land - as the lion with the man, the various forms of wing, or characterizations in their various developments. These were as presentations of those projections that had been handed down in their various developments of that which becomes man - as in the present.
18. We are through.
1 comments:
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