Hi Alex,

First of all a big thank you for all the work that you, Robin and Kanga have done in an effort to understand the inconsistencies in the various surveys. We are all indebted to Stephen Brabin for correcting mistakes in Petrie’s survey of the Giza site layout, and now, for is work on the shafts that Robin linked to. I hope a consensus is reached as its important to clarify these issues. I look forward to seeing any conclusions / summary that results from this discussion.

Back to the dating question.

Alex: “In my opinion, the only solution that will not be selective is to consider each shaft as a whole, calculating its angle from the known position of the entrance (after the horizontal part) and outlet.”


I think we agree that the underlying geometry of the upper south shaft is most likely based on sqd 7 (45 degs). However, at the lower end, after the 1.72m horizontal section, the shaft rises at an angle of 39.2 degs and then at an angle of 50,54 degs after which for the last 42m to the top it rises at an angle of 45 degs.

My hosepipe analogy was meant to demonstrate that whatever happens at the lower end of the shaft - in this case two radical changes of angle - should not be taken into consideration when assessing possible celestial alignments - only the angle of the upper section is relevant as its crucial to determine the area of the sky the top opening of the shaft is facing.

As you point out, Petrie’s angle of incline for the upper 21m section varies over short distances which is only to be expected for the following reasons:

The pyramid is about 4600 years old and has survived earthquakes that may have caused slight subsidence among the individual stone blocks that make up the shaft. The exterior cladding of the pyramid has been demolished that again probably caused slight movements to the upper section of the shafts. The inside of the pyramid above the sarcophagus chamber has experienced many violent explosions when openings were forced through the ‘relieving chambers’ that may have caused movements resulting in slight changes of angle. The builders often had difficulties maintaining a straight line for the shafts and the quality of construction varies from very bad to good that also has an affect on the angles.

For these reasons, its important to ascertain the average angle of incline over a longer distance and not use angles over very short distances relative to the total length of the shaft.

If we use Petrie’s 45.2 degs average angle for the final 21m for an alignment to the 3-star asterism in Orion we arrive at c. 2510 BC.

In your nonselective approach you would “consider” Gantenbrink’s 45 degs measured over 42 m as the correct angle to calculate a date for an alignment to the 3-star asterism in Orion - this gives a date of c. 2550 BC.

Both dates, c. 2510 and c. 2550 BC fall within the historically estimated dates for the construction of Khufu’s pyramid that are supposedly accurate to within +-50 years.


The underlying design of the upper north shaft was most likely based on sqd 11 (32.47 degs) which is close to Gantenbrinks measured 32.6 degs. However, according to Gantenbrink, crucially, the last 11m at the top has a 1.4 deg. shallower average angle of incline of 31.2 degs that gives a date of c. 2588 BC for an alignment to the then Pole Star Thuban at upper culmination due north. This average 1.4 deg. change of incline for the top section of the shaft needs to be taken into consideration when determining which area of the sky the top opening is actually facing.

If we use Petrie’s 31.55 degs average angle of incline for the final 9.5m, this gives a date of c. 2526 BC.

Both the north and south shafts were probably constructed simultaneously around 15 years into the building of the pyramid. Petrie’s survey provides possible dates of c. 2510 BC for the south shaft and c. 2526 BC for the north shaft that are reasonably consistent with not only having similar dates for the simultaneous construction of both shafts, but also with Khufu’s reign.

c. 2550 BC for the south and c. 2588 BC for the north shaft obtained from Gantenbrink’s survey still fall within a reasonable time frame for Khufu.

Your nonselective approach to selecting the angles and determining astronomical dates would mean the south shaft was finished c. 2550 BC and according to you, the north shaft c. 2320 BC, a 230 year difference!


It was entirely fortuitous the 3-star asterism in Orion happened to be 45 degs (sqd 7) above the horizon due south during Khufu’s reign. However in the northern sky, the upper culmination of the then ‘Pole Star’ Thuban did not quite fit the sqd 7 / sqd 11 design (the cosmos is not always in tune with human endeavour), so the master builder adjusted the angle of the upper section of the shaft ensuring Thuban would appear framed within the square opening at the top.


For the south shaft the 3-star asterism in Orion was framed within the square opening at the top of the shaft every 24 hours when it was visible, and twice a year the circular disc of the sun was framed within the square opening when the sun and Orion’s 3-star asterism’s rising and setting synchronised.

The circle within a square motif related to the primary dimensions of the pyramid is key to understanding why the level of the floor of the sarcophagus chamber above the base of the pyramid and the level of the dual shaft system’s intersection with the north and south faces above the base of the pyramid are where they are. The sarcophagus chamber was offset to the south of the east/west centre axis line by 21 cubits and by defining the underlying angles of incline for the dual shafts as sqd 7 and sqd 11, created an elegant symmetry ensuring they would exit the pyramid at the same height.

Link to diagrams: [sites.google.com]


Chris