Hi Alex
> The assumption about a height of the Red Pyramid
> of 200 cubits is used for simplification when
> precision is not needed (for example in wiki) or
> by adepts of round numbers.
Surely precision is always desired where possible?
> In order for the pyramid with the base 418c to
> have a height of 200c, its angle of slope should
> be 43° 44' which is about 1° less than the actual
> (Petrie's 44° 36'; Dorner's 44° 44').
Yes, basically what I've been saying.
> For the given angle of slope the height is 209c *
> tg(44,67°) = 206,58c.
I think we need more reliable data.
>
Quote
The horizontal distance from the centre to
> the 10/7 line, where it cuts the bend is 118
> cubits, or with the root 2 slope it is
> 117.36.
>
> For the Red pyramid with slope of 44° 40' the
> horizontal distance from the center to the casing
> plane at the level of 90c is 117,95c which is
> quite close to 118,16c for the Bent pyramid (55°).
Well something like that.
> When I hear that the ancients wanted to "encode"
> the approximation of the root of two in the
> proportions of the Bent pyramid, I ask what ratio
> they wanted to encode in the proportions of the
> Red pyramid (assuming that two consecutive
> pyramids of one king should be built on the basis
> of similar ideas and principles).
If we suppose that Sneferu's and Khufu's builders maintained an architectural tradition of some sort then, by looking at the latter, we might find clues to Dashur. The geometry seems to show this -
- on the left is Legon's Bent pyramid analysis, in which he draws similarities with Giza - 280/99 to define a Bent base of 362 cubits. The pyramid is given a height of 200 cubits, which is divided vertically into the ratio 11/9 by the bend line A. On the right is the Red, with a base of 418 . This figure is generated by a root 3 relation - 362/209. Moreover a prolongation of the root 3 ratio 97/56 = 485/280 intersects the casing at B. This ratio also defines the height of the Red 205 above base. At the start of building the casing of the Bent, the pyramid form was to be half an octahedron and each face an equilateral triangle - or root 3.
So if one is looking for ideas and principles here you have it - geometry. If the width of the bend line is determined by Legon's scheme the Red cannot simply be an 'extrapolation' of the Bent - the Red side must pass through the bend to an apex 205 cubits above base. I can't believe the builders didn't notice the difference in heights between the two pyramids.
>
Quote
The proposition that Betelgeuse and Alnitak
> culminated on the Meridiam simultaneously in the
> pyramid age, at altitudes similar to the slope
> angles of the Bent pyramid
>
> Chris wrote: "
The earlier ‘Bent’ pyramid is
> orientated about 12’ west of north that
> corresponds to the vertical alignment c. 2630.
> Betelgeuse the uppermost star in the vertical
> alignment was 54.52° above the horizon and
> Alnitak, the middle star, 44.53°. These two angles
> are similar to the angles of incline for the lower
> and upper parts of the ‘Bent’ pyramid. The ‘Red’
> pyramid is orientated about 5’ west of north that
> corresponds to the vertical alignment c. 2590.
> Alnitak was 44.7° above the horizon, which again
> is similar to the angle of incline of the
> pyramid."
>
> As we know the angle of slope for upper part of
> the Bent pyramid is 43°-43.5° while Alnitak had
> altitude 44.53°, more than 1° higher.
> Proposed scheme explains angles of slope of the
> Red pyramid and the lower part of the Bent, but
> does not explain its upper part.
Well, one possible solution is to question the slope of the upper Bent. But make the pyramid higher (say 205) and, while you gain in the star altitude department , you lose the Legon geometry. A tantalizing problem.
Robin