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July 6, 2020, 6:00 am UTC    
February 23, 2020 07:58AM
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]
Subject Author Posted

Red Pyramid - New Geometric Model

Mark Heaton February 16, 2020 05:55PM

Re: Red Pyramid - New Geometric Model

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Re: Red Pyramid - Petrie's slope / error?

Mark Heaton February 17, 2020 04:44AM

Re: Red Pyramid - Petrie's slope / error?

keeperzz February 17, 2020 11:40AM

Re: Red Pyramid - Petrie's slope / error?

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Re: Red Pyramid - New Geometric Model

Spiros February 16, 2020 08:47PM

Re: Red Pyramid - Side Length?

Mark Heaton February 29, 2020 11:25AM

Re: Red Pyramid - New Geometric Model

Hermione February 17, 2020 03:39AM

Re: Red Pyramid - New Geometric Model

Mark Heaton February 17, 2020 05:10AM

Re: Red Pyramid - New Geometric Model

waggy February 17, 2020 12:58PM

Re: Red Pyramid - New Geometric Model

Mark Heaton February 17, 2020 04:04PM

A better way

Hans February 17, 2020 05:33PM

Re: A better way

Mark Heaton February 18, 2020 05:03PM

Re: Red Pyramid - New Geometric Model

waggy February 17, 2020 11:08PM

Re: Red Pyramid - New Geometric Model

Hans February 18, 2020 12:21AM

Re: Red Pyramid - New Geometric Model

Mark Heaton February 18, 2020 07:10PM

Re: Red Pyramid - New Geometric Model (correction)

Mark Heaton February 19, 2020 03:14AM

Re: Red Pyramid - Perring v Dorner Query

Mark Heaton March 10, 2020 03:45PM

Re: Red Pyramid - New Geometric Model

GChase February 17, 2020 05:41PM

Re: Red Pyramid - New Geometric Model

waggy February 17, 2020 11:38PM

Re: Red Pyramid - New Geometric Model

Chris Tedder February 20, 2020 07:57AM

Re: Red Pyramid - New Geometric Model

GChase February 20, 2020 09:37AM

Re: Red Pyramid - New Geometric Model

Chris Tedder February 20, 2020 04:02PM

Re: Red Pyramid - Solar Model

Mark Heaton February 20, 2020 04:49PM

Re: Red Pyramid - Solar Model

Chris Tedder February 21, 2020 12:27PM

Re: Red Pyramid - Solar Model

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Re: Red Pyramid - Solar Model

GChase February 21, 2020 05:37PM

Re: Red Pyramid - Solar Model

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Re: Red Pyramid - Solar Model

GChase February 22, 2020 04:06AM

Re: Red Pyramid - Solar Model

Chris Tedder February 22, 2020 02:20PM

Re: Red Pyramid - Solar Model

Mark Heaton February 22, 2020 05:04PM

Re: Red Pyramid - Solar Model

Mark Heaton February 22, 2020 05:17PM

Re: Red Pyramid - New Geometric Model

keeperzz February 23, 2020 11:06AM

Re: Red Pyramid - New Geometric Model

GChase February 24, 2020 07:54AM

Re: Red Pyramid - New Geometric Model

robin cook February 23, 2020 07:58AM

Re: Red Pyramid - New Geometric Model

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Re: Red Pyramid - New Geometric Model

keeperzz February 23, 2020 10:21AM

Re: Red Pyramid - New Geometric Model

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Re: Red Pyramid - New Geometric Model

GChase February 23, 2020 04:26PM

Re: Red Pyramid - New Geometric Model

robin cook February 24, 2020 09:24AM

Re: Red Pyramid - Dorner's Survey - link?

Mark Heaton February 24, 2020 09:50AM

Re: Red Pyramid - New Geometric Model

GChase February 24, 2020 10:49AM

Re: Red Pyramid - New Geometric Model

keeperzz February 24, 2020 01:26PM

Dorner's Diagrams

GChase February 24, 2020 01:50PM

Re: Dorner's Diagrams

keeperzz February 24, 2020 04:09PM

Re: Dorner's Diagrams

Hermione February 24, 2020 05:21PM

Re: Dorner's Diagrams

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Re: Dorner's Diagrams

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Re: Dorner's Diagrams

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Re: Dorner's Diagrams

robin cook February 25, 2020 04:59AM

Re: Dorner's Diagrams

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Re: Dorner's Diagrams

robin cook February 25, 2020 12:43PM

Re: Dorner's Diagrams

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Re: Dorner's Diagrams

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Re: Dorner's Diagrams

Hermione February 26, 2020 03:38AM

Re: Dorner's Diagrams

GChase February 25, 2020 03:13PM

Re: Dorner's Diagrams

GChase February 25, 2020 05:35PM

Re: Dorner's Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Mark Heaton February 25, 2020 05:59PM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

GChase February 26, 2020 07:51AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

GChase February 26, 2020 09:06AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Mark Heaton February 27, 2020 04:22AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Kanga February 27, 2020 06:10AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

keeperzz February 27, 2020 11:17AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Bent Pyramid Diagrams - Solved ?

GChase February 27, 2020 12:50PM

Re: Dorner's Bent Pyramid Diagrams - Solved ?

robin cook February 27, 2020 02:17PM

Re: Dorner's Bent Pyramid Diagrams - Solved ?

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Re: Dorner's Bent Pyramid Diagrams - Solved ?

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Pistol March 04, 2020 02:51AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

GChase March 04, 2020 08:36AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Chris Tedder March 05, 2020 09:00AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

GChase March 05, 2020 02:55PM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Chris Tedder March 05, 2020 04:20PM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

keeperzz March 03, 2020 03:23PM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

GChase March 03, 2020 06:20AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Kanga March 03, 2020 07:38AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Mark Heaton March 03, 2020 02:19PM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

keeperzz March 03, 2020 03:28PM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Kanga March 04, 2020 07:38AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

GChase March 04, 2020 08:49AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Kanga March 05, 2020 05:51AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

GChase March 05, 2020 06:10AM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

keeperzz March 05, 2020 04:52PM

Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Chris Tedder March 07, 2020 07:51AM

Bent Pyramid lower section

keeperzz March 09, 2020 04:59PM

Re: Bent Pyramid lower section

Kanga March 10, 2020 12:27AM

Re: Bent Pyramid lower section

keeperzz March 10, 2020 05:42PM

Re: Bent Pyramid lower section = Red Pyramid

Mark Heaton March 10, 2020 10:20AM

Re: Bent Pyramid lower section = Red Pyramid

keeperzz March 11, 2020 09:58AM

Re: Bent Pyramid lower section = Red Pyramid

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Re: Bent Pyramid lower section

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Re: Bent Pyramid lower section

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Re: Dorner's Red Pyramid and Bent Pyramid Diagrams

Kanga March 08, 2020 07:58AM

Bent Pyramid - You are all wrong

Kanga February 27, 2020 01:21AM

Re: Bent Pyramid - You are all wrong

GChase February 27, 2020 04:39AM

slope angles

robin cook February 27, 2020 05:17AM

Re: slope angles

keeperzz February 27, 2020 01:02PM

Re: slope angles

robin cook February 27, 2020 04:47PM

Re: slope angles

keeperzz February 28, 2020 06:56AM

Re: slope angles

robin cook February 28, 2020 09:02PM

Re: slope angles / solar model

Mark Heaton February 27, 2020 04:56PM

Re: slope angles / solar model

keeperzz February 28, 2020 03:26PM

Re: slope angles / solar model

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