Did the Egyptians know anything about PI or why 2/3 harmonic ratio fraction was sacred in Egypt....

 So in this fascinating pdf analysis we get a deeper hint 

What the authors do is take the Egyptian directions seriously - thereby constructing the above image.

Notice how fascinating this is! To attempt to "square" the circle as PI does by squaring the radius as an irrational ratio - we have instead an image that shows the rational difference as 1/2 circle of the diameter in a rational segment. In other words - there is a "half circle" phase difference between the rational diameter length and the actual circumference length. Which is to say this "one half phase difference" is the noncommutative geometry of the natural harmonics hidden in the squared pi value.

The West chastises Egypt for supposedly not knowing "pi" as a ratio (assuming symmetric logic) whereas it is the West that does not know the secret noncommutative phase truth of pi. This secret has been rediscovered by converting time-frequency uncertainty of 1/2 spin particles back into radians. So a 1/2 spin particle has to make a 720 degree rotation in order to "return" back to its original spherical source.

https://numberwarrior.wordpress.com/2008/03/05/on-the-egyptian-value-for-pi/

This is a fascinating overview on the origin of PI in Egypt - as a close approximation.

But I have another take on this. The author concludes - no the Egyptians just had a measurement "procedure" and so no real knowledge of "pi" as a transcendental irrational number....

But what are we really talking about? Egypt somehow constructed huge pyramids with a precision that even modern technology can not mimic - when the scale is considered.

We do know that 2/3 was a sacred fraction in Egypt - and my argument is this is due to harmonics and the arguments for the pyramids as sacred harmonic energy resonators has been vast.
So now consider Egypt's "approximation" of PI - 

With simplification it becomes
 

Ok. The deal is that 3/2 squared is 9/4 and halved back into the octave is 9/8 or 8/9 depending on th eharmonic inversion. In other words BECAUSE 2/3 was sacred in Egypt, therefore 8/9 was also sacred.

NOW - the reason this is so important is because "pi" assumes a "symmetric math" logic for squaring the circle - and quantum time-frequency uncertainty has PROVEN this is wrong! In other words a "spin 1" particle is based on classical physics whereas a 1/2 spin particle is a "half quanta" BEFORE converted into symmetric math, and therefore existing in the 5th dimension as non-local wave or phase resonance that is superluminal.

And what is the 1/2 particle but the origin of time-frequency uncertainty due to noncommutative math logic! In other words BECAUSE 2 does not go into 3 - therefore 2/3 is sacred as the nonlocal "yang" - that is in two places at the same time (the undivided yin-yang or the 3 in 1 unity secret).

So you double the radius but then have to "square" it to turn the circle harmonics that are inherently noncommutative into the PI value. But this "squaring" procedure covers up the noncommutative phase secret of the 2/3 that is secret in Egypt! This is the real reason why Egypt did not "understand" PI as a ratio but instead Egypt understood PI as derived from 2/3 noncommutative harmonics.