72 cubits is the module (as 3 X 24 and 33 + 39) of the layout of the upper passages, whose point of origin is the intersection of upper and lower floorlines. Passage junctions were determined by the application of a template derived from the pyramid proportion 14/11 and the double square (11-14-14, etc). The design proceeds in a logical way and gives the locations of many features. So can we now agree that this is the basic design we must start from? (If not, what other scheme offers itself as a serious contender for the prime 'design imperative?)

The 9/11 division in the upper passages is indeed interesting, considering these are also the proportions of the rectangle enclosing the pyramid layout, as well as other features. Additionally the height of the KC complex - from the floor of the KC to the shaft exits - is 154 - 82 = 72. So we have both 72 and 75 - in round numbers.

Various small discrepancies, and fractional dimensions, have been pointed to as evidence of more subtle intentions. Interesting in their own right but sometimes difficult to relate to the overall design, in which the KC floor is located 82 above base by the root 2 operation. Yet Petrie yields 82.1 - error or intent? Then again we take Khufu ideal proportions as 14/11 and base of 440 when, by Petrie's passage cubit of 0.52375m, it is 439.81 - I wonder what the Seked of this is?. (Some say this was a subtle adjustment to incorporate 'true Pi' into the design - with a height of 280 this would have a base of 439.823. Close but no cigar). At any rate the base measure discrepancy is difficult to dismiss as error because of the quality of the work in both the casing and passages - as opposed to the rougher work in the KC complex, upon which Petrie commented (for example the Great Step slopes E/W across its width, while the floor of the KC complex is rather uneven - presumably the result of sloppy work or subsidence). On the other hand we do see variation in the length of the cubit at other pyramid sites so perhaps also at Khufu.

There seem to be three ways of thinking about the situation -

- the builders worked in whole cubits, the slopes of the upper passages are roughly 1 in 2. the AE approach to building resembled a kind of ponderous craft work

- the architects were very clear about their intentions and, by use of a template or 'algorithm', produced fractional dimensions in the upper passages as discussed in this thread

- the architects worked to a 'hidden agenda' where relatively sophisticated mathematical relations involving areas and volumes may only be perceived by descending to the digit level, requiring the pyramid to have been precisely planned throughout

But all this concerns Khufu. Other pyramids appear not to have been designed to the same standard nor are their interior arrangements understood (partly because of the appalling lack of survey data - as Waggy has highlighted). Or (with the exception of Meydum) apparently designed on different principles - Legon showed that passage junctions in Khafre appear to reflect the NS spacing in the layout, rather than a scheme derived from the dimensions of the pyramid itself, as at Khufu. (But then one comes across propositions like this, which argues for meticulous planning at Unas -

[books.google.fi]

What do you make of it?)

While we may agree that a pyramid is a development of the mastaba, and needed to include various features to serve the needs of the cult (serdabs, false doors, and various other chambers whose function we can only guess at), the strict dimensional planning of interior features seems unrelated to these essential requirements. If, as some suggest, a pyramid was a machine to send dead kings to the stars, then why such variation in design? The architects had no way of confirming if a particular design 'worked best'. So there must have been other imperatives in pyramid design. Rather than writing off the builders as hopelessly neurotic, the repetition of numerical quantities in various pyramids suggests some kind of order in the apparent chaos, and our best hope of understanding the thinking of pyramid builders.