I presume your post is directed at mine (even though you are replying to Jim's posting), as you are referring to something that I stated when you wrote "Show me the evidence that proves the Egyptians were aware of Phi, and then you can claim that "phi proportion shows up all over the place".


The phi proportion does indeed "show up all over the place", this is clearly evident from an examination of the survey data.

You have claimed to have found pi in your bathroom - can you show me the evidence that proves the designer or builder of your bathroom deliberately incorporated pi in your bathroom? - of course you cannot, so does this mean you have not found pi in your bathroom as you have claimed? - of course not - its supposedly there according to you, but its just a coincidence.


Egyptologists, Lehner and Badawy, have also found the phi proportion in AE architectural designs, but that is perhaps more of a consequence of the 8:5 proportion that yields 1.6, which is close to the 1.618.....phi value. - it does not necessarily mean the AE knew phi.


After the "phi proportion shows up all over the place", I continued with:

"The question is, were these intentional or are they a consequence of the geometry involved in planning the layout of the interior (scroll down the link to see the idea) - I suspect its a consequence of the geometry - its difficult to know for sure, but in every case, a round of applause for Khufu's son, Hordedef."


Even though the phi proportion is evident in the design, as no explicit textual evidence for AE knowledge of phi is known, it probably means the designers were not aware of phi, it was more likely a consequence of the design rules and geometry they were using - the geometry that uses the square, 1:2 rectangle and circle, as I demonstrated - the level of the sarcophagus chamber above the base of the pyramid is not defined by a seqed.



AS: "B. Show me the evidence that proves the Egyptians used simple ratios to calculate rise over run slopes, and then you can claim that simple rise over run slopes show up all over the place."


No mathematical texts have survived in the archeological record from the Early dynastic Period or the Old Kingdom, but nevertheless, its highly likely the designers used simple ratios for defining slopes and proportion in the OK - how else would they do it?

Explicit textual evidence for seqeds however, is from much later 'mathematical texts', but these texts have examples that the AE were using already in the OK, and the writings of Hordedef, who is a good candidate for the designer of his father's pyramid, were known in the MK.


I think most of us here on Maat agree that seqeds or at least simple rise run ratios defined slopes in the OK, even though there is no explicit textual evidence to support this from the OK - the evidence comes from a careful study of the survey data, but though we have survey data, it needs to be carefully examined, otherwise all kinds of fallacies can be perpetuated, like this little gem from you: "In the Queen's Chamber, which is placed on the center line of the pyramid, the two shafts have the same seqed. Naturally, those shafts would also have exited at the same height, had they required completion."


So what are you basing this on apart from assumptions - there is no way you can be certain of your assertion - the survey data, especially for the lower north shaft is far too uncertain to draw any firm conclusions, and anyway Gantenbrink only measured the shaft up to the first bend - the rest is unknown unless Hawass measured it later, but I have seen no official survey data from him yet.

Gantenbrink states on his drawing concerning the initial angle of incline of the lower north shaft: "still uncertain!" so how can you be so certain the south and north shafts have the same sqd?

The various possibilities for the angle of incline for the lower north shaft are: 37.47 degs (Petrie); 43.60 degs; 33.30....40.10 degs; and 39.12 +- 2 degs (all from Gantenbrink), which one did you cherry pick?

The possibilities for the lower section of the lower south shaft are 38.47 degs (Petrie).......39.61 degs (Gantenbrink), so again, how can you claim both shafts had the same sqd?


Perhaps they were designed to have the same seqed, but you cannot assert they did.



AS: "Seqeds are the proof. Phi is nothing but an artifact of their measuring system... not a goal in and of itself. You have no logical, evidenciary stance on which to make any other case."

Don't you have anything better to do than search for imaginary demons to exorcise? - where am I saying or even implying that phi is a goal in itself, or that phi was known? I am not claiming or even implying either!

CT