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July 6, 2020, 4:40 am UTC    
February 20, 2020 04:49PM
Hi Chris,

I thought others must have come to the same conclusion as Petrie on the slope of the Red Pyramid, but for some reason Edwards and others have expressed the view that the upper slope of the Bent Pyramid was adopted as the slope of the Red Pyramid even though Petrie highlighted Perring's error and obtained very similar slopes for all four sides of the Red Pyramid from its core masonry.

My geometric model may or may not have an astronomical symbolism, but if stars were observed at particular angles then the architect may have devised geometric schemes to express those angles.

The following geometric proposition is extremely close to reality, so much so that I have requested others to determine the bearing and distance of the pole of the Red Pyramid from the pole of the Bent Pyramid:

It is proposed that the arc of a circle with a radius of 25,920 cubits is 25,920/sr44 cubits for an angle equal to the bearing of the Red Pyramid from the Bent Pyramid (west of due north), and that this distance was chosen for the distance of the pole of the Red Pyramid from the Bent Pyramid because this locks in the distance from the mid-point of the north side of the Red Pyramid to the mid-point of the north side of the Bent Pyramid as 25,920 palms, thereby bearing out a most important relationship between the pyramids.

(The location of the Red Pyramid is a natural derivative of the radian, so the pyramid could have been built at any distance from the Bent Pyramid up to 25,920 cubits for which the angle would be the radian, but the distance chosen was for the special case of 1/sr44 which means that the distance is 27353 palms.The distance between the poles could have been made equal to 25,920 palms as an arc of 25,920 cubits x 1/sr49, but this was not the chosen symbolism.)

It is easy to envisage the proposed model by a line of 25,920 cubits (the radius of the circle) projecting due north from the middle of the north side of the Bent Pyramid, but originating from the pole of the pyramid, and a second line of 25,920 cubits (the radius of the circle) from the pole of the Bent Pyramid and passing through the pole of the Red Pyramid at a distance of 1/sr44 x 25,920 cubits.

This model is based on Petrie's model of the Bent Pyramid with a side length of 360 cubits, and Dorner's model of the Red Pyramid with a side length of 418 cubits.

The proposed model accords with reality for Petrie's cubit of 20.68 inches, and there is a simple reason for the model:

In my model of the Bent Pyramid the intended angle was tangent 10/7 before a change of plan, so the angle of the sides to the pole of the pyramid was 35 degrees with the ratio of 35 degrees to 360 cubits (base side length) equal to the ratio of 360 degrees to 25,920/7 cubits. Therefore the decision to build the Red Pyramid at a distance of 25,920 palms (25,920/7 cubits) was associated with the change in plan.

The odd bulge out towards the north end of the Bent Pyramid was because most of the north side had already been completed at the tangent of 10/7 up to a level of 90 cubits when the decision to change the design was made, but very little of the south side had been completed which was built at the reduced slope equal to the tangent of 28/20 (seked of 5 palms).

The theoretical perimeter for the seked of 5 palms is 25,920 digits at a level of 90 cubits.

The rounded effect is more pronounced on the east and west sides showing that these sides had been partly built, much less complete than the north side but much more complete than the south side. The east and west sides had to overcompensate the upper part of the slope (up to the level of the bend at 90 cubits) so that the resultant mean slope is close to the seked of 5 palms. The shape now observed looks like a very poor build standard, but the change in the slope above the level of the bend was accompanied by a subtle change in slope below the level of the bend. It should have been obvious that completing the pyramid in this way would result in an ugly distortion.

Petrie imagined that the same rounded effect applied to the upper section of the Bent Pyramid at the seked of seven and a half palms, but his determinations of the slope at very few positions do not substantiate his proposition. It was, however, reasonable to suppose that this was would prove to be the case with more measurements, but there is now an explanation for the curvature below the bend.

The proposed model incorporates 25,920 digits, 25,920 palms and 25,920 cubits. The lost symbolism of 25,920 palms latent in the original design was replaced by three expressions of this number, but the most important is 25,920 palms. The new model appears to combine two geographical aspects, one looking due east to the horizon from the Red Pyramid and one looking due north to the horizon from the Bent Pyramid.

The height of the Satellite Pyramid (49.5 cubits) is exactly a quarter of the height of the height of the Bent Pyramid (198 cubits) so the Satellite Pyramid was part of the change in plan, and turns out to be a scale model of the Red Pyramid.

There is a strong inference that a decision was made to build the North (Red) Pyramid at the same time as the decision to change the design of the South Pyramid from a true pyramid to a so-called Bent Pyramid, and that the Satellite Pyramid was required to integrate the designs in order to achieve the original purpose of the South Pyramid.

The Satellite Pyramid projects a circle with a circumference of 360 cubits at the centre of the base of the Bent Pyramid, as proposed on this forum about 10 years ago. The radius of this circle now has a projection to 25,920 cubits, and yields an arc of exactly 3168 palms for one degree assuming the circumference of the circle was divided into 360 divisions, as calculated for the pi approximation 22/7.

We have already seen how a cotangent may be related to an angle. A rise of 3168 palms for a run of 25,920 cubits is an angle of 1.000 degrees using modern trigonometry on rounding to 3 decimal places.

This is the basis of my new geometric model of the Red Pyramid as apparent from both the interior and exterior of the pyramid. This model yields the number of days in a year as 365, not the number of years in a notional stellar cycle.

The division of the circumference of a circle into 360 parts is attributed to the Babylonians, but it was a natural division from which to contemplate a year as soon as it was known that there were 365 days in a year. The cycle of time is 360 days plus 5 days in between years.

In my hypothesis Sneferu's South Pyramid would have been a simple model of the solar cycle if it had been completed as a true pyramid. The Bent Pyramid is a model of the solar cycle by way of ingenious projections that were not part of the original design.

In this proposition the shape of a true pyramid is naturally associated with the ascendancy of the solar cult in the reign of Sneferu.

It is not suggested that stellar aspects were rejected, but the 25,920 symbolism is not connected to the circumference of a circle so at this stage there is no evidence that a cycle of 25,920 years was contemplated.


Mark



Edited 4 time(s). Last edit at 02/20/2020 05:15PM by Mark Heaton.
Subject Author Posted

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