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The Great Pyramid at the Giza Plateau, Egypt, is mysterious, mystical and strategically placed on the face of the Earth. It is aligned with the four cardinal points more accurately than any other  structure, even the Greenwich observatory. The builders displayed enlightened understanding of engineering, mathematics, physics and astronomy. They also had a profound knowledge of the Earth's dimensions. Many scientist and scholars now think it was built earlier than the reign of Cheops (Khufu) at 2600 B.C. They disagree with the traditional view of Egyptologist and attribute it to an advanced civilization before the rule of the Pharaohs. I am convinced they are right. For more details follow the "Egypt/Center of Earth" link.
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. It lies in the middle of Egypt and in the middle of Lower and Upper Egypt.
    
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.

Pyramid Statistics  © 2000 by Larry Orcutt,A total of over 2,300,000  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. 

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. 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 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.

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. Geometry of the Great Pyramid 

DIMENSIONS of Great Pyramid

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.


Squaring the Circle

Squaring the Circle

The circle and the square are
united through the circumference:
440x4=1760=2x22/7x280

area of square: 440x440=193600
area of circle:28x28x22/7=246400
sum: 440000

 

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:

dimension
b. inch
m
royal cub.
palm
digit
base
9068.8
230.35
440
3,080
12,320
height
5776
146.71
280
1,960
7,840
sum
 
 
720
5,040
20,160
slope
7343.2
186.52
356 
2,492
9,968
edge
8630.4
219.21
418
2,926
11,704

The Great Pyramid

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, 
280 royal cubits

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. 

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).

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.)

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
By theory of 34 slope to 21 base
Height : circumference :: radius to circle
9 height on 10 base diagonally
7 height to 22 circumference
area of face = area of height squared
(or sine) = cotangent, and many other relations)
2 height vertical to 3 height diagonal
5 height on 4 base

51º 52' ± 2' (51.867)
51º 51' 20"
51º 51' 14.3"
51º 50' 39.1"
51º 50' 34.0"
51º 49' 38.3"

51º 40' 16.2"
51º 20' 25"

** 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... :
(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 practiced 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.


The Concave Faces of the Great Pyramid 


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.

creased sides
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."


concave sides
Diagram of the concavity (not to scale).

What was the purpose for concave Grea the first pyramid should hold true for the others."


concave sides
Three proposed "baselines" of the Great Pyramid (not to scale).

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.

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