Hello Byrd,
Here's the response to your message I wanted to post yesterday, but Life got in the way...
I wrote, ‘3) Multiplication and division by 3 1/7 or 22/7 were used extensively in the planning of Khufu's pyramid and its passages and chambers.
4) Khufu's architect chose Seked 5 1/2 for the Pyramid's slope because he was aware that the diameter-to-circumference ratio he knew as 3 1/7 or 22/7 was inherent in it.
You replied, ‘I would agree with one and two, but not three and four.
They didn't build anything else (or any other pyramids) with those constraints. When civilizations build to a formula (as the Greeks did with the Parthenon and other temples), then we see it adopted and carried forth in everything since then.
I would agree that they used a model of the pyramid and that they measured angles to get the thing just right. But this set of proportions only works with certain building materials and is an utter failure with others.
In engineering problems, the materials constrain the possibilities. If it had been possible to build completely out of granite, you may well have seen a more steeply sided pyramid similar to the ones built in Nubia by the pharaohs – pyramids which very closely resemble the written symbol for "Pyramid."’
I do not know – nor does anybody else - if the multiplication and division by 3 1/7 or 22/7 was used extensively in the planning of pyramids and their passages and chambers other than (as I hypothesise) Khufu's.
The interiors of pyramids did not become more-or-less standardised until the start of the 5th Dyn with Userkaf at Saqqara; prior to then it was very much a case of a pyramid’s interior being laid out according to individual taste.
The slopes of the pyramids from Sneferu through to Khendjer (Lehner
The Complete Pyramids page 17), fall in the range 45 to 57 degrees, with the 4th Dyn favouring 51:50 (Seked 5½) and 53:7 (Seked 5¼).
Because of this, I think it unlikely that the same system of calculating dimensions was used throughout the 4th Dyn (in particular) pyramids – individuality appears very much to have been the order of the day.
I don’t think it is reasonable to draw parallels between the pyramids of 4th Dyn Egypt at circa. 2575-2465BC and the architecture of the Greeks of 5th Century B.C. – two different cultures separated by some 2,000 years.
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I wrote, ‘Now, I see this as consistent with the views expressed by Petrie, Edwards,Verner and no doubt other authorities on the Egyptian pyramids.’
You replied, ‘Remember that it was Petrie himself who called people who tried to find some sort of mathematical schema in pyramids, "Pyramidiots."
Actually, Petrie was referring specifically to the people - such as Piazzi Smyth - who 'found' Biblical dates and geodesic and astronomic data in the Pyramid’s dimensions.
In
The Pyramids and Temples of Giza 1883, Petrie gives a few of his own suggestions on how the dimensions of the Pyramid’s passages and chambers were determined through basic mathematics.
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You continue, ‘I think he would be very scornful of this last bit of reasoning.’
Well, my hypothesis is based almost entirely on a system of basic maths markedly similar to those Petrie suggested the Pyramid’s architect might have used, so I can confidently say that Petrie would like my hypothesis very much indeed - this is not to say he would actually agree with it.
MJ