Hi Jim

You wrote - "I am pretty sure there is a typo in your earlier post about the exit heights of the KC shafts with over 100 inch difference where the 2 is supposed to be a 1. Petrie's diagram gives the north shaft at the bottom of 103 and the south shaft at the top of 103, and Petrie gives 25 inches for the height of course 103, so should be a bit less than 25 inches difference based on his diagram, but the top of 104 is supposed to be the 154 cubit level, so this remains a bit of a problem. In the text Petrie does say S comes out at 104 and N at 103, but that is basically what his diagram shows also".

Well, to reiterate, Gantenbrink, in the 1997 paper he presents on his website, stresses the importance of finding common reference points in the design of Khufu, saying that "The ceiling height of the QC passage constitutes a common quantity at the lower end of the Great Gallery". But is Gantenbrink so meticulous as he presents himself? He states that the Descending and Ascending passages have the same slope, which is not a fact. Also how come he and Legon, both of whom are surely familiar with Petrie's figures, nevertheless promote the 154 KC shaft exit height? If the start of KC south is at 77 vertical and 22 horizontal from centre, and its angle is 45 degrees, it must hit the casing at 154 vertically. Further, Emhotep and Djedi provide little information (eg. "Angles of lower shafts are 'about' 40 degrees"). It is a mess which might be resolved if the authorities would release the detailed information they must possess.
Nevertheless, whatever the geometric niceties turn out to be, I am content that the target star altitudes that Chris has provided support the conclusion that, before all else, these are 'starshafts'. Perhaps the 'two lands' echoed in the 'two skies' - 'as above so below'? Just a thought.

I read your new webpage and found your work on Phi divisions of the Descending passage excellent. Particularly because it dovetails with previous geometric definitions of passage junctions (cf. Legon). So I made a quick sketch to show what I mean -



First, whereas the base of Khufu is not a whole number (if one uses Petrie's cubit) the prevalence of the 14/11 ratio in IVth dynasty work suggests that it is the basis of design - 280 height and 440 base, and a good approximation of squaring the circle. The point of origin of the axis of the Descending passage appears to be defined by the intersection of square and circle at (A). However it is the ceiling of the passage upon which the Phi constructions are made.

As to the upper passages if we begin by making the assumption that it too is laid out on the diagonal of the double square it would appear to have its origin at B, 280 horizontally south of centre and 220 vertically. This line intersects pyramid side at (C) at the same level as defined by your construction on the passage 'vertex' (D).

However the upper passages are not laid out on the diagonal of the double square but at lesser angles and it turns out that prolongation of the ascending passage axis intersects the side of the figure at (E) which is the same as the vertical distance below base as the end of the ceiling of the Descending passage. I do not believe this a coincidence.

I am impressed by the vast amount of work that you have done in analyzing Petrie's measurements of Khufu. Incidentally I came across a Danish site [khufupyramid.dk] which presents no analyses but presents Petrie's figures in excruciating detail - I assume the figures will be the same as yours. But together a useful reference for the rest of us. I also applaud your use of pictures to illustrate your ideas - they say a picture is worth a thousand words and this is especially true on this forum. Few are motivated to wade through convoluted calculations while trying to hold imaginery images in the mind.

Interesting material but not strictly relevant to this already bloated thread and perhaps to be discussed in a new one?

Robin