A Religious Function Expressed with Geometrical Astronomy and Built-in Architecture
by Robert G. Bauval
It is an accepted fact that the design of the Cheops Pyramid – and other pyramids to a lesser degree – incorporates a basic knowledge of geometry and observational astronomy.1 The intensely geometrical shape of the structure, the precision of design ratios, and its accurate alignments along a precise meridian make this a certainty. Many geometricians who have studied the pyramid agree that harmony of angles and dimension ratios is to be found in the design.2 Those who have studied its astronomical alignments generally agree that stellar alignments taken at the meridian were the means by which the base of the monument was set out and, as has been shown,3 the means by which some of the internal features were positioned.4
Above all else, however, the monument is intensely religious, with the main cultic purpose of assisting the dead king in his ascent to the sky.5 In brief, therefore, the monument is a sepulchre with a potent function which, for lack of appropriate terminology, can be said to be astrological.6 This is a widely accepted consensus and is confirmed by the liturgy of the Pyramid Texts.7 The religion and rituals of the Pyramid Age were a sky religion, whereby the king became a star and his star soul became established or transferred to the southern stars of Orion and Sirius and to the northern stars, which included the three circumpolar constellations of Ursa Major, Ursa Minor and Draco.8 The supreme task of the ancient architect was to express these vital elements of the sky religion in the design of the monument. When all is said and done, the pyramid structure was primarily an instrument of rebirth for the departed king.
To achieve this religious function, the architect based his design on simple geometrical principles using right angles and bisected angles fixed with simple mathematical ratios and proportions. This is the common practice in architectural and building engineering design principles, in order to create the ideal functional monument within the constraints of structural considerations and building limitations. Elementary mathematics are bound to be detected by all who study the design of the Cheops pyramid.9 Yet researchers should not imagine that elementary mathematics was an essential aspect of the pyramid cult; it was merely a tool, albeit probably a sacred tool by which the priestly architect could perform his trade.
The Narrow Shafts
There are four narrow shafts in the Great Pyramid, two from the King’s Chamber that emanate northward and southward; two others emanate, also northward and southward, from the Queen’s Chamber. These have been discussed in numerous books and articles since 1837.10 Though they were first thought to be for the purpose of ventilating the internal chambers of the pyramid, the accepted consensus today is that they served a religious purpose of passageways for the ascent of the ‘soul’ of the dead king.11 The present writer is a firm supporter of this thesis.12 There is, however, one main element of the mathematics that needs to be carefully integrated in this thesis if it is to withstand scientific scrutiny: the stellar theory must account for the fact that the architect intended each pair of shafts to emerge at the same horizontal levels on the outside of the pyramid. It is thus important to follow a strategic logic to ascertain, through a series of questions and answers, what the likely intention was of the architect when he opted for this feature.
Mathematical Astronomy or Astronomical Mathematics?
One question that must be answered is: Was the architect briefed to design a monument to express principles of sacred mathematics in the pyramid, or was he briefed to use sacred mathematics to provide the pyramid with features that could service the function of the cult, i.e., to assist the departed king to ascend to the sky?
Perhaps the best way to answer this is to use a more modern analogy. In medieval times (and sometimes still today) cathedrals were designed in the shape of a cross generally orientated east. The main entrance was on the west side, at the foot of the cross, which meant that a congregation entering the cathedral would move eastward, thus symbolising the rising of Christ, the east being the place where the celestial orbs rise as the birth star of Christ, ‘the star of the east’.13 Cathedrals were religious monuments intended to service the liturgical aspects of the Christian religion, and the main briefing given to the architect was based on these requirements. The architect developed his design using geometry and mathematics to express in a symbolic manner the liturgical function of the cult. The cross was designed in geometrical proportions imbued with deep symbolic meaning: the dome represented the sky vault, the altar was the head of the Christic cross and so on. The architect also used simple observational astronomy to orientate the monument eastward: certain panels towards the sunrise or sunsets and so on.
It stands to reason, therefore, that if a medieval cathedral (such as Chartres in France) is scientifically scrutinised, from its design and orientation will be extracted both sacred mathematics and the elements of simple observational astronomy. But to assume that the main purpose of the architect was to express either is misleading. The correct conclusion would be that the architect used symbolic mathematics and observational astronomy to express the liturgical function of the monument.
The same applies to the Cheops pyramid. A scientific scrutiny will extract the principles of a sacred geometry and certain aspects of observational astronomy, but these are only the tools of the architect’s trade and, devoid of religious input, do not elucidate the purpose and function of the monument. A scientific approach is necessary only in that it informs us of the tools and thus of the architectural language through which the religious purpose and function can be understood.
The correct approach to a full understanding of the pyramid design is therefore to make use of elementary mathematics and observational astronomy to extract the symbolic meaning of the design and ultimately link it to the liturgy of the cult. This is also the approach to take in the scrutiny of the shafts in the Cheops pyramid.
A Brief Based on the Religious Function
We know from the Pyramid Texts that both the northern stars and the southern stars were essential aspects of the rebirth rituals and directly related to the celestial destiny of the departed king.14 It has also been shown by many researchers, Egyptologists and astronomers that the constellations in question were:
a) The northern meridional region: those of Ursa Major, Ursa Minor and Draco. The last, of course, had its main star, Alpha Draconis, as the pole star of the Pyramid Age (c. 2500BC).
b) The southern meridional region: essentially, these were the culmination of the constellations of Orion and Canis Major (which contains Sirius). We must add the constellation of Taurus, including the Hyades, which also had important cultic significance.
All stars, of course, have to be precessed and ‘proper motioned’ back to the epoch of c. 2500BC to meet with the assumed date of the Cheops pyramid.
The religious ritual which took place after the death of the king was essentially a rebirth, as we have said. Some have termed it the Osirian Rites, since ultimately the dead king became an Osiris and departed to the celestial kingdom of this god, in the sky region of Orion.15 First, however, a variety of ceremonies had to be performed before the dead king was deemed ready to undertake his journey to Orion-Osiris. The most essential was the opening of the mouth during which Horus and his four sons, with ceremonial cutting instruments, opened the mouth of the Osiris-king to induce its rebirth. This ceremony, too, had strong astral connotations but linked to the circumpolar region of the sky. It has generally been accepted that the two ceremonial cutting instruments were shaped to look like the constellations of Ursa Major and Ursa Minor.16 Another major part of the event was the symbolic birth of a new Horus (the new king), which also had a stellar connotation as ‘Horus who is in Sirius-Isis’.17
We can therefore safely conclude that the architect’s brief was to incorporate in the design of the rebirth chambers architectural elements which would service the essential rituals of the opening of the mouth, the birth of ‘Horus who is in Sirius-Isis’ and, ultimately, the departure of the soul to the celestial kingdom of Osiris-Orion. In previous articles18 it was shown that the two southern shafts pointed to Orion’s Belt and to Sirius, mythologically Osiris and Isis respectively. The two northern shafts were directed to the pole star, Alpha Draconis, and to the head of Ursa Minor, the celestial adze of Horus, also called the ‘adze of Upuaut’.19 All these alignments work for the same precessed epoch of c. 2450BC plus or minus twenty-five years.20
Tools and Techniques of the Architectural Design
In considering the techniques of design, we must define the context of the architect. Historically, we are looking at c. 2500BC, when the two pyramids at Dashour and that at Meidum were completed by King Sneferu, father of Cheops. The experience acquired in true pyramid design and construction would obviously be related to those pyramids. In accepting that the architect of Cheops used basic geometry to define the scale and proportions and basic observation astronomy to align the base and other features such as the shafts, we must also accept that he had a wider vision based on the past geometrical and astronomical design of the Dashour pyramids and a future vision of the Giza Necropolis as a whole.21 All these elements had to be linked in one unified architectural vision which, if correct, would be visible in the integrated design and layout of the Dashour and Giza pyramid sites and, ultimately, in the design of the pyramid of Cheops.22 The final product, the design of the Cheops pyramid had to be linked with the religious purpose of the monument.
25. The astro-geometry of the shafts and chambers inside the Great Pyramid, with the upper culmination position of the stars taken C.2450BC
All measurements are in royal cubits. 1 royal cubit = 0.5237 metres