I tend to agree that we should consider the geometry first, which may then provide a reason why the geometry was chosen.

For example, the niche in the so-called Queen's Chamber was probably for the king's statue or ka statue, and is displaced from the centre of the chamber by eight and a half palms or 34 digits, precisely so based on Petrie's measurements near the base, so by 25.03 inches for a cubit of 20.61 inches or 635.7 milimetres for a cubit of 523.5 millimetres, which Smyth had measured as 25 inches and then supposed that this was a ten millionth of the Earth's semi-polar axis (6357 kilometres), but there is a better astronomical explanation from the angle of the shaft of the Queen's Chamber.

The seked of eight and a half palms is 39 degrees 28 minutes, so very close indeed to 39 degrees 30 minutes as reported in 'The Orion Mystery' with the shaft supposed to point to Sirius.

The notion that pyramid shafts could be used to fix the age of the pyramid supposes that the architect aligned the shafts to particular stars, capturing a picture of the ancient heavens monumentalised in stone, but perhaps the shafts only needed to point in the general direction of the intended star.

The first annual appearance of Sirius at dawn in ancient Egypt is now known to correspond to a cycle very close to 365.250 days, so not the solar cycle of 365.242 days, or the cycle apparent from more distant stars.

It is reasonable to suppose that Sirius was regarded as a marker of the solar year, rather than the calendar year of 365 days, because it is the brightest 'fixed star' (as opposed to wandering stars now known to be planets in orbit around our own star, the Sun).
The ancient mind presumably saw all objects appearing to be stars as stars, and the Sun and Moon as entirely different.

There is a potential connection between 365 days and a length of eight and a half palms.

The east side of Khufu's pyramid was probably built first. The side length at the base was intended to be 440 cubits. The position of the corner sockets underlying the base square was determined by J. H. Cole most precisely (and without any theory) nearly a hundred years ago. The extra length results in 44.5 digits on the south side (83 cm) plus 45.5 digits for the north side (85 cm), so a mean of 45 digits or 90 digits in total.

A length of 440 cubits plus 90 digits equates to 365 multiplied by eight and a half palms as the horizontal distance which can be regarded as borne out in the angle of the shaft pointing to Sirius.

The east wall of the Queen's Chamber leans in 1/25 x eight and a half palms, so 34/25 digits (25.4 millimetres). Smyth did not observe the lean-in which was determined by Petrie, and converts to just over an inch as a projection to the ridge of the roof (angle close to 14 arc minutes).

I proposed a pyramid theory at the Second British Egyptological Conference at Liverpool in 2008, showing how the lean-in of the east and west walls of the Queen's Chamber may be regarded as projecting a vertical height of 1460 cubits interpreted as a cycle of 1461 calendar years of 365 days in 1460 solar years of 365.25 years. The Egyptian lunar cycle explains why the Egyptians did not adopt a leap year. The base of the triangle is not far below the floor of the Queen's Chamber, so the intersection of the KC shafts below the floor of the King's Chamber is an interesting proposition with the potential for a secret crypt below the floor of the King's Chamber.

A length of 365 x eight and a half palms equates to 9125 multiplied by the lean-in of 34/25 which is the number of days in the Egyptian cycle of 309 lunar months in 25 calendar years.

The east-west floor length of the Queen's Chamber is 309 digits (or 365 digits to the back of the niche), and 365 x eight and a half palms (34 digits) is the east side length of the corner sockets, with no need for a square of the corner sockets because the lunar cycle is 25 calendar years not 100 years.

The exit height of the Queen's Chamber South Shaft is not relevant, because the shafts do not exit the pyramid, although might have done so if the upper chamber (the King's Chamber) had not been completed due to unforeseen construction difficulties.

The exit height of the King's Chamber Shafts may have had some geometric property, and rather than trying to piece a complicated picture unifying the interior of the pyramid to the exterior of the period we can rely on Petrie's survey which describes how he determined a rigorous connection between the exterior of the pyramid and the interior for the entrance passage, and then applied the same principle to a projection of the King's Chamber shafts; see page 17 of 1885 edition for a simple explanation in order to know where the shafts would have emerged from the pyramid which inevitably did not occupy a whole case because the shafts are so small.

Quote from Petrie page 17 of second edition:

The north channel cannot by its position have come out in any but the 103rd course, and the south channel in any but the 104th, they would show that the casing rose on the north face at 51 degrees 51 minutes and 30 seconds and on the south face at 51 degrees 57 minutes 30 seconds.

This was a rigorous assessment not susceptible to all sorts of potential errors by trying to calculate the exit positions based on the entire internal configuration of the pyramid.

Petrie's meticulous methods have not been repeated for other pyramids, such as the Red Pyramid, so the relationship between the exterior and the interior has not been determined rigorously.

It should be appreciated that the excellent diagrams of Robin Cook cannot capture the slope of the northern shaft in the King's Chamber which has to twist around the Grand Gallery, so the slope reduces if the slope is constant in the cross-section because the distance travelled is greater rather like weaving from side to side when cycling up hill so as to reduce the slope.

The position of the KC north shaft in the chamber was clearly important otherwise it would have been placed where it did not have to veer off course around the Grand Gallery, and this may have a bearing on what was around the Grand Gallery (the void theory).

In short the exit positions of the shafts are known most precisely, and the positions within the King's Chamber are known most precisely with short horizontal sections.

The floor level of the King's Chamber was intended to be 82 cubits according to Petrie (I agree), so it seems likely that the pyramid builders compensated for any build errors by ensuring that the shafts came out at the required courses from which you can calculate the theoretical slope in cross-section.

From memory the length of the passage from the Great Step to the King's Chamber is 365 digits plus the length of the Great Step which is governed by the structure of the south end wall and very nearly 3 cubits. The mid point of the King's Chamber is another 5 cubits, so the mid point of the King's chamber is just over 21 cubits, but it may be that the intersection of the projection of the shafts is not in the middle, and I think the diagram showed 22 cubits as a little off centre.

If you apply the line of reasoning from the Queen's Chamber to the King's Chamber, then geometry rules the design, but may also have had an underlying stellar, lunar, or solar significance borne out by other geometric features of the pyramid.

The King's Chamber geometry is akin to the Queen's Chamber geometry, because the perimeter of the long walls may be regarded as a circle with a radius of 10 cubits and squaring the area of a circle with a radius of 10 cubits for the pi approximation 22/7 corresponds to a square with a side length of 365 x 34/25 digits, so the perimeter of the square is 1460 x 34/25 digits, so a cycle of 1460 days from the lunar model of the base square, which is 1 day short of 4 solar years. The King's Chamber cubic diagonal is 25 cubits and 25 x 365 x 34/25 digits is the east side length of the pyramid (from the north east corner of the north-east corner socket to the south east corner of the south east corner socket).

The Sun and Mood were more important to the king's after-life than the stars, but the stars were important

Mark



Edited 7 time(s). Last edit at 10/17/2020 04:05AM by Mark Heaton.