Hi Kanga

You seem to be sympathetic to the idea that Khufu was designed geometrically and that shaft angles were adusted to target stars which, at this epoch, serendipitiously had altitudes evoking the pyramid's geometry - as a way of linking the earth to stellar mythology I suppose.

Butler states that "the descending passages in the Meydum Pyramid, Bent Pyramid, Bent subsidiary Pyramid, Second Pyramid, and Third Pyamid were also doubly bent". (To which might be added Khufu's descending passage - bent at the junction of the rock-cut and built portions). Well, the survey data for pyramids not surveyed by Petrie remains somewhat shaky (as Hamilton has observed), Butler seems largely to rely on the figures of Maragioglio and Rinaldi. But putting this aside, if these other passages also pointed at stars what were they? Does 'Djoser's box' point to a particular star? (Uncertain dating certainly doesn't help). (btw Legon presents his proposition for the bend in the Bent west passage here -
[www.legon.demon.co.uk] )

As to the geometric aspects of the design the chambers and passages appear to have been laid out with reference to the fundamental proportions of the pyramid, as much discussed on this forum. For example the elementary root 2 division of the height to locate the floor of the KC uses the same proportion that appears in Gantenbrink's analysis as 280 / 198. The centre lines of Gantenbrink's shafts converge 77 cubits above base and 22 from the centre. But what exactly is the crucial position of the break in angle further up the shaft? Where does Gantenbrink give this information on his site? Perhaps that Djedi site presents better data, I must check.

I mentioned that KC north shaft in plan is not parallel to the meridian but veers by a few degrees to the east (after the bend to the west to avoid the Grand Gallery). But all passages are constructed in the east half of the pyramid (I had intended to put up this plan which originated with Gantenbrink here but I've also got computer problems - I used Imgur for years but it has changed and I can't find the format for a bulletin board link. Getting old I guess). The divergence is too large to dismiss as sloppy work, and it is difficult to relate to known geometric schemes. If it targets Thuban then this would not be at culmination. What then?

I have experimented with your scheme for KC exit levels, and while your vertical dimension from Ascending/Gallery floorline junction to north shaft exit is indeed 110 cubits and is relatable to the 440 base and 88 sloping length of the Gallery, the only connection I can see with a 'virtual pyramid' of base 200 and height 127.3 would be the 100 cubit dimension from the Gallery junction horizontally to the centre of the KC.

I'm afraid I don't agree with your statement - "It was all a very elaborate plan to set traps for the unwary". I can understand that in later times, when tomb-robbing was rife, king's might have wished to conceal their tombs. Rather, in the great pyramid age, they surely wished to appeal to the gods rather than presenting them with problems to solve. The game is still afoot and the best thing I can do is to seek out more solid data (and see if I can find a better picture-hosting site).