Various writers have previously mentioned this 7 : 11 ratio for the exterior of the pyramid. In fact, it is even in Petrie’s Pyramids and Temples of Gizeh amongst many others. And the 7 : 11 ratio of the Great Pyramid’s external casing stones has occurred because the pyramid is constructed using the mathematical constant, Pi, as a model or guide.
The simplest Pi ratio that maintains whole-number values on both sides of this mathematical constant is 7 : 22, and it was from this ratio that the 7 : 11 ratio for the pyramid’s external dimensions was drawn. The increase from 11 to 22 is due to the formula for a circle being multiplied by 2 (ie: 2 x Pi x r).
However, the complete solution to the small shaft riddle came when it was noticed that the numbers involved in the shaft angles, also embody these very same Pi ratios (both the angular elevation, and the linear dimensions of the shafts). The shafts themselves deviate up and down by a few tenths of a degree, but the average trajectory is quite reliable. If we assume that the architect was only constructing angles to the nearest 0.5°, the angles involved in the four small shafts that branch off from the Great Pyramid’s main chambers are 45°, 39.5°, 39.5° and 32.5°. *2
And if we plot those angles and lengths on a cross section of the pyramid, something interesting happens - the rise in each shaft is exactly 70 Royal or Thoth cubits (tc). And 70 tc is exactly 1/4 the 280 tc vertical height of the pyramid itself. So the linear dimensions of the small shafts, including their all-important vertical rise in cubit lengths, are mathematical and intimately related to the cubit dimensions of the pyramid itself.
The vertical rise of the small shafts is 70 tc in each case,
or 1/4 the 280 tc vertical height of the Great Pyramid.
The remarkable symmetry of the shafts of the Great Pyramid
And while this is all quite clever, there is more to this shaft symmetry, much more. If we subtract the larger angle from the smaller angle on each side of the pyramid (the north and south sides), the numerical differences between the angles are as follows:
45° minus 39.5° = 5.5° 39.5° minus 32.5° = 7° The value of 5.5 is obviously 1/4 of 22.
Surprisingly, here are those same Pi ratio numbers yet again (7 : 11 or 7 : 22), but here they are involving angles, not lengths. Again, the complex nature of these shaft angles can be seen. They not only produce linear dimensions that are intimately related to the dimensions of the pyramid, but the numerical differences between their angles is also intimately related to the dimensions of the pyramid. This is a surprisingly complex thing to achieve, especially as the starting point for all these numbers is fixed by the mathematical constant, Pi ! This is achieved in part because the pivotal angle of 39.5° can be derived from (2 x Pi)2 , and also from the arc-sine of 7/11 (or 1/2 Pi).
Debunking the theory that pit heading for the stars
And the really important outcome of all this surprising mathematical symmetry, is that it totally destroys the star-shaft pointing theory. Readers can clearly see that the lengths and angles of the small shafts in the Great Pyramid use the mathematical constant Pi as their fundamental design criteria. They are Pi-based shafts. But this means that their angles of elevation are fixed by Pi, and not by the position of a particular star in a particular era.
A Pi shaft angle cannot point at a particular star; it can only ever point at a fixed angle, and so any star-pointing can only be random. But if you are allowed the freedom of changing the era, which changes the angle of elevation of the star via precession, then of course you can make the star-pointing theory fit. If we discovered a shaft angle of 55°, this would equate to the position of Orion in about 4450 BC. And so we can continue, ad infinitum, for any angle and any era. The star-pointing theory is infinitely flexible, and therefore infinitely false.
Source: Ancient Origins