robin cook Wrote:

> I have come across suggestions for the use of
> Pythagorean triangles by the AE, for example in
> the layout as put forward by the late Clive Ross

Rossi (Arch. & Math. in AE, pp. 216-221) also puts forth a number of triples "possibly employed" in AE pyramid construction - the 3-4-5, 20-21-29, 8-15-17, 5-12-23 and 7-24-25. These are all "true" triples. She does not seem to have looked into the "empirical" triple possibilities.

> By the way, where do the 68.72-99 and 49-50-70
> triples occur?

Petrie (A Season in Egypt, p. 27) felt that "the likely rule" for the exterior slope of the Red Pyramid was the "slope of 7 on a base of 5" right triangle. This is the 49-50-70 empirical triple. Petrie erred slightly in ascribing a 44°34''40" angle to this slope - it is actually nearer 44°25'16". His main point, though, was that the intended exterior slope angle definitely was not 45°, as others such as Dorner have proposed.

I have argued elsewhere that this pyramid may well have been intended to incorporate a host of empirical triples that all hover around the 43° to 45° nexus. These triples would have included the 68-72-99 (i.e., 17-18-24.75), as well as Petrie's 49-50-70, the 90-91-128, and even possibly your 99-99-140 - among others.

> Returning to the question of Khufu 'design
> choices', as you put it, my take is as follows -
>
> The key ratios are 14/11 and 140/99, shown here in
> the layout of the KC shafts -

Note that the 14/11 ratio also stems from an empirical triple - the 55-70-87. Your 140/99 stems, of course, from the 70-70-99 empirical triple - joining together the most important numbers of 70 and 99 in one assemblage.

> At any rate the integrated nature of Khufu passage
> design puts paid to the conceit that small
> differences can be ignored. The upper passage
> slopes are rigorously defined by horizontal and
> vertical dimensions which are fractional. The
> passages were not all intended to be laid out on a
> 1 to 2 rectangle.

I again agree completely with what you say here. And thank you for sharing your analyses - I find them all very interesting.

In rereading my earlier post on this thread I notice that I misremembered the attribution of one of my favorite Holmes quotes - "Singularity is almost invariably a clue". This comes from The Boscome Valley Mystery, and NOT from Scandal in Bohemia. This is such an important truism that I couldn't let my lapse go uncorrected - Oh the shame and embarrassment of it!





Edited 1 time(s). Last edit at 07/10/2018 02:47PM by L Cooper.