Part 1: The 'Shafts First' Solution
This article represents – in part – a response to John Legon's paper, 'The Geometry of the Air-Shafts'  in which Legon dismisses the idea that the shafts within the two chambers of the Great Pyramid of Giza were targeted at particular stars, whilst asserting that the function of these shafts were intended merely as ventilation channels.
In particular, this article will challenge Legon's main argument against the star-shaft hypothesis, proof of which he asserts lies in the geometry of the Great Pyramid itself. As Legon puts it, "…we find that the alignments of the shafts fall into place as an immediate development of the most elementary pyramid geometry." This article will show how this proposal is erroneous and will present a radical new proposal for the purpose of these most enigmatic of pyramid features.
In his paper, 'The Geometry of the Air-Shafts' Legon writes:
"…Owing to the random disposition of the stars in the night sky, however, we should not expect that an alignment to a star of cultic significance in the southern sky would have required the same angle of inclination as an alignment to a cult star in the northern sky; and this in itself is a strong argument against the star-shaft hypothesis. Again because the Queen's Chamber is situated in the mid-plane of the pyramid, the equality of the angles means that the shafts would have emerged at the same level in the casing on the north and south sides of the pyramid – a design of no consequence for star-shafts…."
That the designers should wish to target particular stars solely for "cultic' reasons is also an erroneous assumption. The Queens Chamber shafts certainly could have targeted 2 stars of identical (or near identical) inclination but it should not be inferred that this would automatically have been for 'cultic' reasons. These 2 stars at near identical inclination could just as easily have been chosen in order to form the basis of the pyramid design itself – as we shall shortly see. Indeed, that the Queen's Chamber is placed in the mid-plane of the Great Pyramid is central to this idea. In effect, the dimensions of the Great Pyramid are a direct consequence of the geometry of the star-shafts, thus it can be argued that the star-shafts can be deemed the key element of the Great Pyramid design and of primary significance to our investigation.
"…At a first approximation, one obvious requirement which was satisfied by these angles [of the shafts] was that the shafts should take the shortest route from the Queen's Chamber to the outside of the pyramid. In the context of the 'ventilation' theory this makes perfect sense, since the shortest distance would have provided the most effective air-flow…"
Legon is assuming here that – in the design phase – the Great Pyramid slope (seked 5.5) was selected first and that the angles of the shafts were chosen only afterwards. Naturally, it would follow that if the slope angle of the pyramid had already been decided, for the shafts to then reach the pyramid's exterior quickly and efficiently as possible, then the angle of those shafts should be placed at right angles to the pyramid slope (or as near to this as was practical).
On the surface Legon's criticism of the stellar hypothesis seems perfectly logical. It seems to indicate that the ancient designers were more obsessed with a particular mathematical angle than a particular set of 'cult stars'. However, what Legon has failed to do is to consider the inverse situation with regards to the wider stellar hypothesis, asking the obvious question: what if the primary design element was not actually the Great Pyramid slope but was in fact the shafts and, more specifically, the angles at which those shafts are inclined? If this were the case then it logically follows that the dimensions of the Great Pyramid would have been determined from the shafts and not the other way around as all commentators, including Legon, have long assumed.
Indeed, even from an orthodox perspective whereby it has been proposed that these shafts were 'star shafts' or indeed 'soul shafts' which aided the dead King's soul to target and ascend to particular locations in the northern and southern skies, Legon's argument makes little sense.
The idea that the original purpose of these shafts had something to do with their possible alignment with the northern 'circumpolar stars' (known as the "imperishables" because they never set) and the southern 'setting stars' (which never rise) was first put forward by scholars Alexander Badawy and Virginia Trimble in 1964.
More recently, writer and researcher, Robert Bauval suggests that the shafts were 'stargates' constructed to guide the dead Pharaoh's soul to the heavens. However, like most theories, this conclusion has had its fair share of critics who are right to inform us that:
1) No stars can be seen through the shafts as the angles of the shafts are irregular.
2) The shafts are horizontal for a short distance where they begin from the chambers.
3) Two of the shafts – those exiting the Queen's Chamber – don't even reach the pyramid's exterior and as late as the 19th century were sealed also within the so-called Queen's Chamber.
Bauval is adamant that he is right and that these alignments of the shafts are of a symbolic stellar nature.
Bauval tells us that first the southern shaft of the King's Chamber (45º) aligned with the star Al-Nitak in the constellation of Orion around 2,475 BCE. This is long after the reign of the fourth dynasty pharaoh Khufu who is said to have reigned between 2,589 and 2,566 BCE, and whom Egyptologists believe had ordered the construction of the Great Pyramid for his own personal tomb. Bauval says that at this time Al-Nitak within Orion's Belt, was crossing or transiting the Giza Meridian at 45º exactly.
Bauval then informs us that the northern shaft of the King's Chamber (32º 28') aligned with the Polestar Thuban in the constellation of Draco around 2,425 BCE. There is no date given for the northern shaft of the Queen's Chamber that Bauval says aligned with the star Kochab in the constellation of Ursa Minor. Finally, Bauval states that the southern shaft from the Queen's Chamber (39º 30') aligned with Sirius around 2,400 BCE.
Clearly there is a problem here, because the lower levels surrounding the Queen's Chamber would have been constructed before the upper levels surrounding the King's Chamber. However, we are being told that the shafts from the King's Chamber were meant to align with Thuban and Al-Nitak before the shafts of the Queen's Chamber were meant to align with Kochab and Sirius.
Furthermore, it is suggested by some Egyptologists that the so-called Queen's Chamber was constructed only as a 'stand-by' chamber should the builders have failed in their greater goal of constructing the main King's Chamber higher up the pyramid. This idea, however, seems to be contradicted by the angles of the shafts which are significantly different in the King's Chamber to those of the Queen's Chamber. This proposal would seem to imply that Khufu apparently changed the stellar destination of his soul during the construction of his pyramid and thus changed the angle of the King's Chamber shafts to reflect this change of mind.
Oddly, however, Khufu continued constructing the Queen's Chamber shafts long after this apparent change of mind. It seems somewhat peculiar that Khufu would continue to construct the Queen's Chamber shafts (at the very same time as the King's Chamber shafts were being constructed) when it seems that he had already changed the stellar destination for his soul as evidenced by the changed angle of the King's Chamber shafts. Why continue to construct the 2 Queen's Chamber shafts when these apparently had been superseded by the new stellar destination implicit in the changed angles of the King's Chamber shafts?
From what we now understand, it is tempting to agree with Bauval and his predecessors on the theory that the shafts do indeed have some kind of stellar association. However, although Bauval's own thesis is interesting, the order in which he places these dates leave room for some doubt which leads us to take the view that there has to be some other stellar connection with the shafts of the Great Pyramid.
Due to the work of German explorer, Rudolph Gantenbrink and the small robot he constructed to explore these shafts, it has so far been found that some two-thirds up along its length, the southern shaft exiting the Queen's Chamber had been purposely blocked by two "doors" or limestone plugs some 5 inches square. First there was the discovery of the first door which immediately caused a media sensation. This door was later breached by sending a robot up the shaft with a drill attached so as to make a hole big enough in the door to pass a camera-eye through. But once through, a second door was found. At present, Gantenbrink's work continues to see or go beyond these "doors", and to discover what might lie on the other side, and it has been theorized that a chamber may indeed exist at the end of the shaft. At the time of writing, this remains to be seen. In any case, as a result of Gantenbrink's fastidious explorations, all four shafts have now been carefully tracked, meticulously examined and measured from inside; every twist and bend recorded, analysed and assessed . . . however . . .
Everyone seems to be searching for a 'practical' purpose for these shafts. They point out that no light can shine down these shafts and no one can see the stars through these shafts anyway – as if this is in itself a revelation. Amazingly, this fact is still being used to explain away the 'star-shaft theory' even though Bauval has stated many times that these shafts were symbolic – inasmuch as they "guided" the dead Pharaoh's soul to the stars.
Surely, however, if the King wanted his soul to reach particular locations in the heavens then his architect would have FIRST measured the inclination of these celestial locations and then ensured that the shafts that were eventually to be built into the body of the pyramid were angled at these precise inclinations to facilitate the correct ascent of the King's soul to the desired celestial locations. However, if as Legon proposes, the shaft angles were determined purely around the practicalities of reaching the exterior of the pyramid ABOVE and to the DETRIMENT of the King's desire that they should be best angled to enable his soul to ascend to particular celestial locations, then the King's soul might never reach its intended destination in the heavens.
Bauval's view that the four shafts guided the soul of the pharaoh to the stars is supported by what is described in the Pyramid Texts. It could also be argued, however, that the purpose of these shafts was to attract or perhaps 'extract' the magical essence of these stars associated with what they stood for in terms of magical correspondences and deliver their empowering energy, as was believed, to the pharaoh whose body occupied these chambers and whose soul was believed to have travelled to and became these stars – all highly symbolic.
But concerning the shafts themselves, perhaps we should all stand back a little and take a more "lateral" perspective as it were. In our view, the initial purpose of these shafts is that they may have been intended by the designers to be viewed as "pointers" to the stars – more like the indicators and "arrows" we see in drawings and diagrams which are used to point out the more significant features.
The shafts are pointing out the stars that the ancients wanted us to recognise . . . as the inclinations of these stars are part of a very simple and logical 'message'.
Contrary to the on-site, hands-on, archaeological approach, these particular star constellations and their most important stars – which have now been brought to our attention by these shafts – can only really be seen from the modern "armchair" view of a cross-sectioned map or plan of the Great Pyramid against the background of the stars in the night sky.
Now, however ironic and incongruous this might seem, we must never overlook the work and dedication of those archaeologists and researchers whose time and effort was spent mapping the Great Pyramid from every point and angle so as to provide us with this internal view.
We would suggest that it was intended – indeed hoped – that a future civilisation such as ours would view the Great Pyramid precisely in this way – a view that would most certainly have been familiar to those who had first drawn-up the blueprint for this colossal 'time-capsule;' a repository of knowledge that could withstand the ravages of time.
The Shafts First
The 'Shafts First Hypothesis' (SFS) proposes that the angles of the star-shafts within the Great Pyramid of Giza were the primary and critical design feature that the ancients sought to "set" in stone within the body of the Great Pyramid. From this premise it logically follows that the angle of each of the Great Pyramid's slopes – 51.84º – could be viewed as simply being the result of squaring the angle of the two fairly equally inclined shafts of the Queen's Chamber (see figure 3).
The 'Shafts First Solution' also explains precisely why 2 stars of identical (or near identical) inclination would (by necessity) have been sought by the designers – not for 'cultic' or other esoteric reasons but for reasons of ensuring a symmetrical, 'balanced' design of the pyramid structure. This is not to say that symbolic aspects to the angle of the stars chosen by the ancient designers did not feature in the structure – there most likely were symbolic aspects to the shafts and these will be discussed later.
In consideration of the 4 shafts within the Great Pyramid, it stands to reason that the inordinate amount of resources and effort that would have been required to place these quite unique features within the body of the pyramid lends considerable weight to their primacy and paramount importance within the pyramid structure. Simply put, the Great Pyramid may have been constructed in order to "carry" the 4 shafts.
This idea is most certainly radical and far-reaching. Undoubtedly some will even consider it ludicrous. The Shafts First Solution turns our whole view of the Great Pyramid design and, indeed, it's very purpose quite literally on its head. What possible reason could there be to construct a structure such as the Great Pyramid around 2 sets of 2 shafts? What was it that was so important to the ancient designers and builders about these shafts that they should expend so much blood, sweat and tears to ensure they were built into the body of the Great Pyramid?
The answer is perhaps remarkably simple. The 4 shafts of the Great Pyramid might not have been designed as conduits of air as Legon and others have proposed, but rather as conduits of information; of knowledge. Like a notebook is designed to allow us to place information within its pages, so the Great Pyramid was designed to carry vital information through its 4 shafts – like "arrow" pointers. The difficulties the builders would undoubtedly have faced in constructing the pyramid around these shafts demonstrates a clear spirit of purpose and determination that could only have been matched by the seriousness and importance of the information – the 'message' – the shafts carry.
"…The slope of the shafts would also have encouraged the setting-up of convection currents, causing hot spent air to be drawn out of the chamber while allowing cooler air to take its place…"
Quite simply, with regards to the Queen's Chamber shafts, this idea can in no way be considered the purpose of these shafts for one very simple reason: the Queen's Chamber shafts were – until the 19th century – sealed at both ends. There was never any intention on the part of the designers or builders of these shafts ever being used as air conduits. Legon concedes this point but attempts to rationalise it by citing the 'symbolic significance' of the shafts and of how the Ancient Egyptians could have secured their [air-flow] function through 'magical means'.
This reliance on symbolism and AE magic to explain away the obvious fact that the Queens shafts were never intended to act as air conduits seems somewhat contradictory on Legon's part given that, in the very same paper, he dismisses Bauval's stellar hypothesis on the basis that it relied upon what Bauval described as 'sacred mathematics' being used to achieve a 'religious function'. Essentially then, Legon offers no explanation for the Queen's Chamber shafts.
As previously stated, however, the shafts do indeed serve a practical purpose and also contain certain symbolic aspects such as the sealing of the two shafts at both ends, which will be explained shortly.
"…Now to obtain the shortest possible length for the shafts from the Queen's Chamber to the outside of the pyramid, the incline of the shafts had to be made equal to the inverse of the pyramid's casing-angle…The line of the shafts then intersected the face of the pyramid with an angle of 90°. The mean angle of the two shafts as observed by Petrie corresponds to this profile with a difference of only about ten minutes of arc: Angle of Slope, for 11 rise on 14 base = 38° 9' 26". This same basic angle of slope might also have been used for the shafts leading from the King's Chamber, if it were not for the fact that this chamber was set entirely to the south of the pyramid's central axis. If the same angles had been employed, the shafts would have come out at different levels on the pyramid's north and south sides. It was evidently to avoid this outcome that the builders compensated for the offset of the chamber, by increasing the angle of the southern channel while reducing the angle of the northern channel by a similar amount…"
In this passage there is no attempt made by Legon to explain why the builders chose to offset the King's Chamber from the pyramid's central axis, skirting over this very obvious anomaly as though it was of no consequence. Further, Legon also fails to attempt to explain the curious elevated roof of the King's Chamber which seems to defy all manner of explanation. These aspects of the internal design of the Great Pyramid are important "clues" that Legon has overlooked in his analysis.
Legon comes to his conclusions by assuming that the internal chambers were set in place first with the shafts being afforded only secondary consideration. It is entirely possible however, that at the blueprint stage, the designers of the Great Pyramid set the shafts in place first and placed the mid-plane of each chamber through the vertice of each set of shafts i.e. the point where the lower ends of the (extended) shafts would intersect. But this, of course, raises the next obvious question: why is the vertice of the upper shafts from the King's Chamber not aligned on the pyramid's central axis like those of the Queen's Chamber?
Why did the designers place the vertice of the upper shafts off-centre (by some 6.5 degrees), thereby off-setting the King's Chamber from the pyramid's central axis? The answer to this question lies in how the Great Pyramid was designed and what that design was intended to convey.
The Stellar Pyramid Design
As indicated earlier, it is possible that the Great Pyramid was designed using two stars of similar inclination – one in the northern sky, the other in the southern sky. The following diagrams demonstrate how this is achieved:
STEP 1a: The 'target' stars' inclinations are measured (Queen's Chamber Shafts)
Figure 1a – The Inclinations of Stars are Measured and Recorded
STEP 1b: The 'target' stars' inclinations are measured (King's Chamber Shafts)
Figure 1b – The Inclinations of Stars are Measured and Recorded
STEP 2: The star 'trajectories' are placed on a central axis
Figure 2 – The Shafts are Set in Place through a Central Axis
Note how the 2 lower trajectories (Queen's Chamber Shafts) are of almost identical inclination and how the upper trajectories (King's Chamber shafts) are slightly offset from the central axis. From this very simple starting point we can now define the slope, height and width of the Great Pyramid.
STEP 3: Two squares are set on the angle of the lower shafts.
Figure 3 – The Angles of the Queen's Chamber Shafts are Squared
Note how these 2 squares set on the lower shafts are bound by the central axis and the length of the upper shafts.
STEP 4: The apex of the pyramid is set
Figure 4 – The Apex is Defined from Two Squares
The apex of the pyramid is now set (by the square of the angles of the Queen's Chamber shafts), thereby setting the slope of the pyramid which is a little under 52° (being the inverse of the lower shaft angles at around 38º).
However, we have still to determine a height and width for our pyramid. This is done simply and easily using the angle of the left upper-shaft (King's Chamber south) which is inclined at almost exactly 45° which is equal to Pi/4. It has often been commented that the Great Pyramid's height to base ratio is equal to Pi/2 with the tan of 4/Pi being equal to 51.85° which is almost precisely the slope angle of the Great Pyramid. This would seem to indicate then that a circle was involved in determining the Great Pyramid's height and base.
STEP 4a: The apex of the pyramid is set
Figure 5 – The Angle between the Shaft Vertices is circa 6.5°
Note how the angle between the vertices of the 2 sets of shafts is set at almost 6.5 degrees. This angle is almost identical to the mean difference in the angles of the northern and southern star shafts and is absolutely key to the design of the Great Pyramid at Giza.
We can check the difference in the star inclinations using the data presented by German researcher, Rudolph Gantenbrink:
|Northern Shafts||Southern Shafts|
32.6° ( 57.40°)
39.12° ( 50.88°)
Difference = 108.28° – 95.35° = 12.93°
= 12.93° ¸ 2 = 6.465°
STEP 5a: Determining the pyramid height and base width
Figure 6 – The 45°Line of the King's Chamber Shafts Extended to Central Axis
STEP 5b: Determining the pyramid height and base width
Figure 7 – A Circle is Circumscribed Around Apex
STEP 5c: The slopes of the pyramid are then extended to intersect the circumscribed circle.
Figure 8 – The Great Pyramid Slopes Intersect Circle
STEP 5d: The pyramid base is now defined.
Figure 9 – The Great pyramid Base is Now Defined
STEP 5d: The Great Pyramid has now been defined by its Star Shafts.
Figure 10 – The Great Pyramid with Star Shafts
(Click on the link below for a full presentation of the Shafts First Solution).
It can be demonstrated, therefore, that the star shafts of the Great Pyramid can be used in a simple and systematic manner to define the actual dimensions of the Great Pyramid itself.
"…The stellar-alignment hypothesis would have been immeasurably stronger if the angles of the shafts could only be expressed in terms of some arbitrary mathematical ratios, for which no obvious geometrical design could be determined; but when the southern shaft was simply aligned along the diagonal of a square, as Bauval acknowledges, how much significance can be attached to any star that happened to pass over the shaft-exit when at culmination? …"
The significance of the star shafts is the simple fact that they may well have been the underlying design imperative of the Great Pyramid. Their significance is perhaps not so much in targeting specific "cultic" stars at their culmination, but in the angles the shafts present, as well as the mean difference of 6.5 degrees in the angles of the northern and southern star shafts, which by the way is also confirmed by the 6.5-degree offset positioning of the King's Chamber shafts from those of the Queen's Chamber, and that in these angles and their 6.5-degree differences there lies a possible "message".
Legon goes on:
"…According to the air-shaft theory, however, the architect was free to determine the angles of slope which best suited his development of the geometrical design, within the broad framework dictated by the need for a short route to be taken to the outside of the pyramid…"
It is, however, equally possible (as we have seen) to turn Legon's conceptual design on its head and suggest that, via the Shafts First Solution, the shortest route for the shafts to reach the exterior of the pyramid would be to design a pyramid whose slopes would be at right angles (or as close as possible) to the shafts. In this way the integrity of the desired angles of the 'star shafts' is maintained (for the King's soul) whilst simultaneously ensuring that the most efficient path of the star shafts through the pyramid course layers is obtained.
"…It turns out that the geometry of the air-shafts is a function of the meridian cross-section of the pyramid itself, and can be developed simultaneously with the geometrical placing of the King's Chamber which I have previously described. At the same time, the positions of the shaft outlets can be shown to have been worked out in whole numbers of cubits, in perfect harmony with the proportions of the pyramid…"
The "meridian cross-section" identified here by Legon would simply be the natural outcome of the Shafts First Solution as demonstrated.
The Primacy and Significance of the Star Shafts
As stated earlier in this article, the Shafts First Solution advances the primacy of the pyramid shafts and suggests that their significance lies in the information they "carry". But what possible information could the 2 sets of shafts carry?
The answer is simple – angles. Or – more specifically – the inclination angles of 2 stars. But why only 2 stars when there are 4 shafts? In the stellar hypothesis advanced by Robert Bauval, it is believed that the shafts target 4 stars (2 north and 2 south) c. 2,500BCE. It may, however, be the case that the 2 northern and 2 southern shafts were designed to target the same 2 stars – one star in the northern sky and one star in southern sky. But why 2 shafts (north and south) to target the same single star (north and south)? And how is it possible to target the same 2 stars (one north, one south) at the same moment in time (and from the same location) when the lower star shafts have different angles of inclination to the upper star shafts?
The answer to this apparent enigma may lie in one of our most ancient world 'myths'. It is a myth that is prevalent in just about every civilisation and culture of the ancient world. It is a myth spoken of in numerous ancient texts, including the books of the Old and New Testaments. This 'myth' tells us in unequivocal terms that in remote antiquity the 'sky fell' and that the stars moved out of their place.
Of course, it is unlikely that the actual sky literally fell. If, however, the Earth's polar axis made a sudden and dramatic shift, this would give the apparent illusion that the stars in the sky had "moved out of their place"; the sky would appear to have "fallen". Stars that once were viewed at a particular elevation above Giza would have "moved" as a result of such a tilt of the Earth's polar axis.
It is proposed then that the angular difference between the 2 sets of shafts in the Great Pyramid suggests that such an axial shift – if this is indeed what occurred in our remote past – demonstrates an axis shift of around 6.5° in a north to south direction. Thus we may find an explanation as to why the shafts in the Queens Chamber are sealed at both ends, failing to reach the exterior of the pyramid. The symbolic message is clear – the stars that once were 'targeted' from these lower shafts can no longer be targeted from those shafts. They have moved – metaphorically – "out of sight" and can now only be targeted from their new location – i.e. metaphorically "observed" – from the upper shafts of the King's Chamber.
One further piece of evidence in support of the axial shift hypothesis that can be gleaned from the angles of the Great Pyramid shafts relates to the apparent "crossover" of the 2 northern shafts whilst there is no such crossover of the 2 southern shafts. The significance of the crossover of the northern shafts tells us that the axis shift occurred in a counter-clockwise direction.
Were the shafts of the Great Pyramid to have targeted 4 individual stars this could have been achieved simply and easily in the manner shown in Figure 11, with no crossover of the northern shafts.
Figure 11 – The Northern Shafts Could have been Designed with no Cross-Over
However, the builders of the Great Pyramid sought to angle the northern shafts in such a way that the angles "cross-over" (figure 12).
The "cross-over" is the tell-tale 'signature' (i.e. the natural outcome) one would expect to find by targeting a stellar location that has moved from one position to another as would be the case in a change of the Earth's polar axis (figure 13). Had the change in the Earth's polar axis occurred in a clockwise direction then we would likely have seen a crossover of the shafts occurring in the 2 southern shafts with no crossover of the northern shafts.
Figure 12 – The Northern Shafts with the Cross-Over
Figure 13 – The Stars Move Out of Their Place
But could this really be the "information" the shafts of the Great Pyramid are telling us, that a shift of the Earth's polar axis took place in remote antiquity? Is there any other evidence available to us that might indicate the same "message"?
It would appear there is.
In Part 2 of this investigation, the authors will examine other aspects of the Great Pyramid and its design that would seem to lend weight to the idea of the Great Pyramid having been erected as a monument to tell of a tilt of the Earth's polar axis in great antiquity.
The authors would like to extend their gratitude to Rob Miller for checking the veracity of the geometry of the 'Shafts First Solution' presented in this article.
- J.A.R. Legon, ‘The Air-Shafts in the Great Pyramid’, DE 27 (1993) [back to text]
- R. G. Bauval, ‘The Orion Mystery’, (1994) [back to text]