A couple of years ago there was a discussion on this site about the Dashur pyramids and their base sizes. The bulk of egyptological references quote values around 0.523 to 0.525 metres for the length of the royal cubit, but Petrie decided that the Bent measured 360 cubits (at the level of the pavement) implying a cubit of 0.526 metres, which is outside the accepted range. Petrie's measure of the Bent base is 189.46 metres (7459 inches)), translating into a base of 362 cubits of value 0.52337 metres - within the normal range. Dorner's figure for the base is very similar (showing that he and Petrie were measuring the same thing) - his figure is 189.61 metres giving a cubit of 0.52378 metres. So I conclude that the base of the Bent was intended as 362 cubits.

For the Red Dorner gives 219.08 metres, or 418 cubits of 0.5241 metres. But a base of 420 defines a cubit of 0.5216 metres; while using Perring's measure for the base of 219.28 metres the cubit would be 0.5220 metres. Both of these are too short. However, Waggy studied the dimensions of the chamber system of the Red and discovered that it had apparently been planned using a very short cubit of 0.522 metres, so if the base was laid out using the same cubit then a base of 420 becomes acceptable. But if this is true what were builders up to? Why use different cubits for two pyramids which (according to authors like Monnier) were built to the same design? Does it mean that the builders were less concerned about the absolute value of the cubit and worked with a local variant?

All over the net, 360/420 - 6:7 is quoted for the ratio between the base sizes, with identical height of 200 cubits. But with the Bent being 362 cubits the scheme does not work. However 362 does make sense because it relates to the dimensions of the enclosure as Legon showed, and involves similar geometric operations to those found at Giza. Khufu being Sneferu's son we might expect some aspects of design philosophy would be shared by both. So I tried to put together a scheme from a strictly geometrical point of view that illustrates this connection -



The side of the square (the Bent enclosure) measures 560 cubits (a dimension celebrated at Giza). The lower part shows the plans of 4 pyramids, and the upper part their sections - K - Khufu. R - Red. B - Bent. M - Meidum.

Khufu and Meidum relate as 8 : 5 as is well known. Using the 420 model, Khufu and the Red relate as 220 : 210 (or as 20 : 21). The 418 model gives the ratio 220 : 209 (20 :19). Favouring the latter is the fact that the base dimension of the Red at 418 can be derived from the Bent base 362 through the root 3 construction 362 / 209 = root 3 (shown in red in the lower right quadrant of the figure).

An operation on the diagonal of the square of 560 (280, 140) divides the diagonal into two parts, 140 and 256, and defines the base of the Bent as 362.
The lower slope of the Bent is root two, so if continued at this angle the pyramid face would be an equilateral triangle. Following the theme of root 3 the classic construction is shown for an equilateral triangle of side 560 (reflecting the close approximation 97/56 (485/280). Thus the apex of the triangle is 205 above base. If this is taken as the apex of both Bent and Red pyramids (with bases 362 and 418) then it is found that the profile of the Bent (brown) intersects the profile of the Red (pink) 90 cubits above base, and this is the bend line. The slope angle of the Red and top of the Bent being around 44.5 degrees. But we can argue about angles till the cows come home (or until proper surveys are done on these pyramids).

Whether or not this scheme is true it favours the idea that the two Dashur pyramids were designed together. Problems arise when we speculate why this was done. Monnier goes along with the well known idea that emerging weaknesses in the structure of the Bent caused the builders to lower the intended slope - the lower part of the bent contains about 8 million cu.Rc and 3 million more would have been required to project the sides to an apex. (The present upper part adds 0.5 million cu.Rc). But this contradicts his statement that the Red profile was the one that the builders 'wanted all along'. In fact they started the Bent to make a pyramid with equilateral triangle faces and only later changed the slope (and manner of building). The implication seems to be that they started all over again at the Red (poor old workers), but why not just complete the lower part of the Bent until it had the same profile as the Red if that was what they really wanted? Something does not compute. And how can we be sure that 'emerging weaknesses' were responsible for the change of slope - Waggy has argued that the dislocations in the passages, supposed harbingers of impending doom, are imaginery.

Different propositions have been put forward to explain the angle of the Red and upper Bent - 3/Pi, the upper face as a segment of a pentagon, and various numerical ratios and so forth, but these do not relate to the profile of the lower Bent as far as I can see. In fact the only hypothesis that does relate the two slopes is Chris Tedder's finding that the altitudes of target stars in Orion correlate with these slopes - if the concept of vertical star alignment is accepted. (But can other pyramid face slopes be correlated with stellar events?). Using conventional dating this backs up the idea that the shafts in Khufu are essentially 'starshafts'. But Alexander Puchkov has cast doubt on the conventional dating which has not yet been resolved.

By the way I remembered that Allison had written about the idea that the Dashur pyramids were positionally linked and found (on that other forum) a discussion on this subject from 2007 -
[grahamhancock.com]