Ronald: "On a vast plain on which more than one monument, having a quadrangual base, has been built, geometry is automatically created."
I'm not familiar with C. Wayne T's idea, and I don't have time to study it, but as a general principle, does your comment mean that its not worthwhile to examine the Giza site for intended spatial / positional relationships?
If after examining the survey data, someone suggests a proposal for an intended formal site plan that ensured an ordered development of the family necropolis (father, a son, and a grandson), and which seems to go beyond mere coincidence, then the proposal should be checked to see if is reasonably consistent with the survey data. If it is, the proposal can then be assessed to see how more or less likely it is that it was intended, and if it was the result of a gradual development where the architects planned a new funerary complex with a formal spatial relationship to existing structures / places, or did it develop according to a pre-determined site plan.
Some object to the idea of a pre-determined formal site plan that incorporates more than one royal funerary complex by arguing its a cultural impossibility - no trans-generational projects in AE, or that the layout was solely dependent on topographical constraints so it cannot possibly conform to a predetermined site plan. These concerns have been addressed in previous discussions.
Some thoughtful comments by Jaromir Malek, an experienced Egyptologist - an expert on the Old Kingdom:
"........... I have little doubt that there was a definable positional relationship between the Giza pyramids, and I am also convinced that a working hypothesis about a similar arrangement at other sites is worth investigating. The difficulty lies in establishing the reasons for such relationships. In my view, there are two main lines of approach.
4.1. A relationship due to ideological (religious) considerations; the pyramids were ideological statements just as much as they were royal tombs. Several hypotheses immediately offer themselves, and I shall mention only three which strike me as the most plausible:
4.1.1. A relationship to the local cult centres (e.g. a need for an unobscured line of vision or orientation, or an imitation of the plan of the cult centre).
4.1.2. A relationship to the monuments already on the site (attempts to create ideologically significant groups).
4.1.3. A relationship based on astronomical alignments or such considerations (reflections of an astronomical features or occurrences).
None of these requires an advance ground ‘master plan’; the relationship might have been built up gradually.
4.2. A relationship created as the result of the planning and surveying methods and of the modular approach used by the pyramids’ architects. Astronomical as well purely mathematical factors could have played a part or been introduced, possibly even unintentionally. Even here, the relationship could have been formed step by step and does not prove the existence of a plan determined at the outset.
As always, it is impossible to prove the presence of symbolism without recourse to other sources, and theories seeking to discern it in the ground plan of Giza must remain highly speculative.
The case for a definable relationship of the three pyramids at Giza is overwhelming..........
...........The idea that the distribution of the pyramids is governed by definable ideological (religious, astronomical, or similar) considerations is attractive. After all, if there were such reasons for the design of the pyramid and for the relationship of monuments at one site, why should we shut our eyes to the possibility that similar thinking was behind the apparently almost perverse scatter of the pyramids over the Memphite area? The argument that the Egyptians would not have been able to achieve this had they set their mind to it cannot be seriously entertained." (‘Discussions in Egyptology’ 30, Malek 1994: 101-114)
link: [
www.hallofmaat.com]
Another experienced professional Egyptologist has even used the term 'Master Plan' in the context of the pyramid fields of Giza and Abusir:
Miroslav Bárta: "As at Giza, the Abusir pyramids of Sahura, Neferirkara and Neferefra were very likely built (i.e. situated in the necropolis) according to a single master plan. Verner was able to show that their northwestern corners lie in a line which runs directly to the northeast and intersects the Giza pyramids line precisely at Heliopolis, in the sun temple of Ra (Verner 2002, 302––3)." (Miroslav Bárta, 'Location of the Old Kingdom Pyramids in Egypt', Cambridge Archaeological Journal 15.2, 2005: 186)
"It is therefore appropriate to ask, in a landscape as prospect-dominated as the Nile Valley, which sites and monuments were mutually intervisible and whether their respective locations, horizons and vistas are owed to something more than mere coincidence." (‘The Topography of Heliopolis and Memphis: Some Cognitive Aspects’ David Jeffreys)
CT