Hello Graham,

Hello Graham,

You write, "There would be no reason why the Egyptian would design something we thought primitive just as there would be no reason why a modern would design something we thought primitive."

Basic arithmetic and linear geometry are widely still in use today in our technologically advanced cultures (ask the professional carpenter who earlier this year built a walk-in cupboard in my flat/apartment ), so I see no reason to think of the AEs use of them as in any way 'primitive'.

You write, 'So if we are going to keep Egyptian geometry simple I don't think we should discard the golden section.'

I am not advocating the discarding of anything.
AFAIK, in Khufu's pyramid there is only one clear-cut example of the possible intentional use of Phi (the Golden Section) in its planning, and that is in the King's Chamber.
Now, this supposed deliberate appearance relies on a) either the distance between the base of the King's Chamber's walls and the surface of its raised floor or the distance between the surface of its raised floor and the top of its walls (one being a natural product of the other) b) the length of the Chamber c) the width of the Chamber and d) the full height of its walls.

Question, how did the architect go about creating the appearance of Phi in the King's Chamber?
I think we can safely presume he started with the floor plan, making it a rectangle 10rc x 20rc.
But what did he do from there on?

To say that the 4th Dyn. Egyptians knew the ratio Phi and deliberately incorporated it in their planning of the King’s Chamber requires, IMO, mathematical proof that its appearance cannot be down to an accident of design.
Now, I have found three ways of reproducing the KC Phi effect or a dimension very close to it.
Only one of these three methods involves the deliberate application of Phi.
The other two create the effect as a natural product of other things.
I suggest that this indicates that the appearance of Phi in the King’s Chamber is unintentional.

IIRC, Phi can also be found in the Pyramid’s superstructure (I can’t recall offhand how it goes).
But again the situation is that it can be shown to be the natural product of something else.
In this instance, simply building a pyramid with a rise of 1 royal cubit to 5 ½ palms run produces the effect.

IMO, keeping ‘pyramid geometry’, to coin a phrase, simple does require the exclusion of the Phi ratio.

Regards,

MJ


Note:
Unfortunately, the actual floor of this Chamber is tilted (NE corner to SW corner, IIRC) by more than 2 inches.
Consequently, it is difficult to tell what the intended distance between the base of the walls and the surface of the floor was (using the top of the first wall course as a guide it is actually from 4.1" to 6.39", or 5.25" +/- 1.15").
Measurements gleaned from the flooring between the King’s Chamber and the Great Step, the face of the Great Step itself, the Grand Gallery ramps, the step in the Queen’s Chamber Passage, and the Queen’s Chamber doorway suggest that the floor of the KC was planned to be 0.27 royal cubits (5.6”) above the base of the Chamber’s walls.
This 0.27 royal cubits is simply the difference between the vertical and perpendicular heights of a passage 2.286 royal cubits high set at a 1:2 gradient.