Just to the south east of Giza there is a rocky knoll, overlooking the Muslim cemetery called Gebel Ghibli (or Qebel Quibli - spellings vary). Lehner commented that it would have been ideally situated to oversee building operations. Some years ago, on this forum, Hale drew attention to this knoll, showing that an equilateral triangle could be constructed between it and the centres of Khufu and Menkaure -




He further showed that the apex of the triangle could also be defined by a simple construction on the centres of Khufu and Khafre, and a 345 triangle -




I noticed that the point of convergence, horizontally to Khafre centre, measures 1314.5 and this = 5.5 X 239. The 'base' of the 345 triangle hence measures 985.9. (Khafre's profile is of course a 345 triangle.)

But 985.9 is also the north south distance from Khafre east/west axis to Khufu sea level north base -




- the diagonal of the square of square of side 1314.5 (239) is 929.5 (169), divided by the line from the NW corner of Khufu in the ratio 7:4 = 591.5 : 338.

Khafre east/west axis to Khufu sea level base is 985.9, and to Khufu limestone base 896 - thus producing the ratio 11 : 10 -




- the line from the NW corner of Khufu intersects the west side of the diagram to define the granite base of Menkaure. The rectangle measuring 836.5 X 1314.5 has the proportions 7/11. The diagonal distance between pyramid centres is divided in the ratio 11 : 10.

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The numbers presented in this series of posts derive from Petrie's survey and a 'reference datum' 114 below Khufu base. This datum, sea level or no, makes mathematical sense, and the plan is seen to be based on the square and its diagonal, quantified according to an understanding of what later became known as Theon's series.

This analysis is limited to those parts of the complex for which good data is freely available, namely Petrie's figures for the interior of Khufu, and for Khafre and Khufu dispositions. We await good data for Khafre and Menkaure interiors, and for other features. Even so there are clues - for example, Lehner gives the original length of the Sphinx as 137 cubits, or one third the base of Khafre (411), thus establishing a link between the two. (And it would be interesting to confirm the height of Zoser base above 'sea level'.)

Here and there are uncertainties and discrepancies - what is the precise height of Menkaure for instance? But at this stage it is perhaps most useful to look at the numbers - do they appear to be logically derived? Or can it be demonstrated that they are coincidental? Questions regarding why or how they would have embarked upon such an ambitious project can wait.

I see Giza as a work of abstract art. We not know the extent to which it's architects 'bought in' to the prevailing superstitious paradigm, or believed that certain combinations of form and number could launch a king's soul to heaven. But they seem essentially to have thought like metaphysicians, or 'proto-pythagoreans', and using geometry as symbolic metaphor. I remain astounded.