Graham: "In its simplest form two squares on top of each other are enough to pinpoint the Kings. It only requires one drawing"
The probable level of the now missing 'Queens chamber' floor was about 41 cubits above the base of the pyramid - halfway between the base of the pyramid, and the floor of the sarcophagus chamber, which is at a height of about 82 cubits - but why would the designers draw two squares with sides of 41 cubits to determine the level of the sarcophagus chamber?
Why 41 cubits, or why 82 cubits - what is so special about these numbers? - perhaps there is nothing special about them - perhaps it was not the numbers, but the method of determining the level of the sarcophagus chamber that was important - using the circle and square.
The position of the sarcophagus chamber within the superstructure had to be determined somehow, so how was the position of what is arguably the most important chamber in the pyramid, determined?
The circle is the simplest regular shape to draw - all that is required is a post, and a length of cord - the cord is fixed to a vertical post, pulled taught and a circle scratched (inscribed) into a stone surface (a square or rectangle by comparison, is far more worksome to draw).
The brightest celestial body in their sky, the Sun (ra), appears as a circular disc in the sky. The horizon is circular, and the Akhet was associated with the horizon - Khufu's pyramid was called Khufu's Akhet. A star within a circle was the hieroglyphic determinative for Duat. About 2750 BC, the top end of the upper northern shaft was facing an area of the northern sky where the then Pole or North Star, Thuban, appeared at upper culmination. Thuban closely marked the pivotal point in their sky around which the northern 'Imperishable Stars' (circumpolar stars) traced a circular path without setting.
The circular Sun, Akhet, Duat and 'Imperishable Stars', were all important components of the royal afterlife beliefs, so it should come as no surprise the circle may have been used in the architectural design of Khufu's Akhet - the level of the sarcophagus chamber can be determined very simply with a combination of circle and square, and not only the sarcophagus chamber, but the exit heights of the upper shafts connected with the chamber.
An example of a circle set within a square is this Dyn 5 offering slab built of stone:
CT