Byrd: “Why wouldn't the masons have finished the chamber while it was still visible and open to the sky? Surely that makes more sense -- the light's better, there's better access to tools, more people can work there. It's not an underground pit.”

Ideally it's easier to work on the chamber in daylight and with plenty of fresh air. However, the chamber was most likely filled with timber scaffolding for the workers who helped manoeuvre the large granite wall blocks into place that prevented the masons from finishing the work inside while construction was in progress. Once the walls were built the roof beams were then levered, hauled and slid into place on a plaster slurry from both ends of the chamber. This would have begun as soon as the walls were finished as the levels of the pyramid were continually rising up over the chamber.

How do we account for the fact that the chamber and sarcophagus are not finished? Traces of 15 bosses or lugs (used when hauling the blocks up onto the pyramid) on the face of the granite blocks still remain on the lower courses of the walls:

“Among peculiarities of work still remaining, are the traces of 15 bosses or lugs on the faces of the granite blocks , all on the lower course. Those best seen are two on the fourth block of the N. wall, counting from the door; they have been about 12 inches wide and the same high, 14 inches apart, and their flat bottom edges 3 inches from the base of the block. They may be very plainly seen by holding a candle close to the wall below them; this shows up the grinding around them, and the slight projection and very much less perfect grinding of the sites of the bosses. There is a remarkable diagonal drafted line across the immense block of granite over the doorway; it appears not to run quite to the lower corner on the E. side; but this is doubtless due to the amount by which the block is built into the E. wall, thus cutting off the end of the diagonal line. This sunken band across the stone appears to have been a true drafted straight line cut in process of working, in order to avoid any twist or wind in the dressing of the face; this method being needful as the block was too large to test by the true planes otherwise used.” Petrie 1883: pp.82-83

The sarcophagus also remained unfinished which implies the masons ran out of time as they rushed to complete the work right up to when Khufu died.



Byrd: “Khufu had a mortuary temple and a valley temple. He must have had a very important-looking funeral with hundreds of participants. The burial party that descended with his sarcophagus probably didn't stay for any length of time.”

The burial party first ascended, then descended, then ascended before finally reaching the sarcophagus chamber high up in the superstructure and over 100 metres from the only source of fresh air, which is a much longer distance than the other pyramids. Heat rises which means the air in the chamber is much hotter than a chamber below the pyramid where it was normally located. The temperature in Khufu’s subterranean chamber “is always 10 - 20 degrees cooler than the chambers situated in the superstructure.”

The sarcophagus chamber has a 55 square metre floor area that can accommodate 40 to 50 people. The funerary party present when Khufu’s physical remains were placed in the sarcophagus took part in the final ceremonies associated with the royal burial. 40 - 50 people would significantly raise the temperature in the chamber and with many oil lamps burning also deplete oxygen. The funerary party was probably made up of Khufu’s close relatives his many sons and families, priests etc. We do not how long the burial party stayed in the sarcophagus chamber, but the final act of burying Khufu was an important element in the overall funerary ceremonies and most likely not rushed.


Byrd: “And the air shafts were blocked, so the incense smoke could not have risen to the sky from inside the pyramid... a detail that surely the architects and everyone else knew.”

We do not know if the upper shafts were blocked or not. Both shafts reach the outer core masonry and are open to the air that effectively provided fresh air to the chamber even before mechanical fans were installed, and would also have allowed incense smoke to exit the pyramid. We do not know if the shafts continued through the casing stones or not. Presumably the ventilation/incense function was a temporary solution and a small opening (22cm square) in the outer face of the casing stones could have been plugged later.



Byrd: “There's no evidence that they knew any geometry nor any reason for them to use a circle within a square…….”

Although no mathematical papyri have survived in the Old Kingdom, the pyramids scream geometry.

The floor plan of the sarcophagus chamber has a simple width/length ratio of 1:2 (10 x 20 cubits), but the 11.18 cubit height of the chamber ensures the three dimensional space is defined by 3:4:5 triangles. Lepre also noted that the largest granite wall stone in the chamber located above the entrance has a height width proportion defined by the 3:4:5 triangle. The geometry that defines Khafre’s pyramid next to Khufu’s is also based on a 3:4:5 triangle.

According to Lauer the plans of three Dynasty 6 mortuary temples and pyramids are based on the 3:4:5 triangle.

Byrd: “……..That said, you can construct any square you like and then draw a circle around it... but it's a pretty meaningless exercise.”

The ancient Egyptians of the Old Kingdom would probably disagree with you.

For example, a large Fifth Dynasty alabaster offering table from the open court in the sun-temple of Niuserre at Abu Ghurab, has a circle within a square theme.
The ideogram for 'offering slab' (R4) is repeated four times to form a square enclosing the circular centrepiece of the flat offering table (sAw). The circular stone offering slab probably references the circular disk of the sun.

The upper south shaft is facing an area of the sky where the circular disc of the sun appeared twice a year. The designer at the design stage could have visualised this occurrence as a circle within the square opening at the top of the shaft.

A 440 cubit diameter circle within the 440 x 440 square base of Khufu’s pyramid (drawn to scale obviously) enabled the architect at the design stage to simply fix the level of the all important sarcophagus chamber and a 280 cubit diameter (the height of the pyramid) circle within the 440 x 440 cubit square base enabled the designer to fix the level of the upper shafts where they intersected with the face of the outer casing.
In both cases, the circles intersect with the diagonals of the square and when lines projected up from these intersections onto a vertical north/south section through the pyramid both levels are fixed.

A circle inscribed within a square relationship defines the 51.84° (sqd 5 1/2) angle of incline of Khufu's pyramid.

Archimedes noted that: “the area of the circle is to the square on its diameter as 11 to 14.” The 14:11 height to half base ratio defines the basic form of Khufu’s pyramid - the base of the pyramid had sides 440 cubits long (40 x 11) and the height 280 cubits (20 x 14).

A consequence of the 14:11 height (280 cubits) to half base (220 cubits) ratio means the height is identical to the radius of circle with a circumference equal to the perimeter of the square base of the pyramid. This is true when a good approximation for the ratio of the circumference of a circle to its diameter (22/7) is used.

Why the 14:11 ratio found in the basic form of the pyramid is a question invariably raised at this point. Gay Robins in ‘Discussions in Egyptology’ suggested a plausible explanation that it derives from “the relative heights and widths of risers and treads in the steps of the Maidum pyramid core and the pyramid of Djoser.” This maybe is true, but the question is still unanswered - why choose a 14:11 ratio in the first place?

Chris