Chris: "Undoubtedly geometric/mathematical based designs underly the design of pyramids - the question is, which of the many schemes researchers have come up with is the correct one?"
Uncertainty regarding the original design of the Bent pyramid exists due to the inability to accurately identify the angles of slope planned by the builders.
I propose so far to leave aside all the debates regarding the reasons for the appearance of dual-slope design (originally planned or not) and consider the lower section separately.
Two features can be noted:
1. The lower faces are convex.
[data by Petrie - A season in Egypt]
However, in some places the faces are flat (marked in green).
The question arises: was such convexity planned by the builders, as Legon suggests, or was this an undesirable effect and the faces should be flat? (Dorner believes that faces were deformed due to irregular shrinkage of the foundations).
Obviously, if Legon is right, then the average value for the lower and upper parts of the lower section should be considered as the angle of slope of the lower section, and if Dorner - the values of the angle of slope near the base only.
2. The lower part of the S. face has a half degree less slope than the lower parts of the other faces (see table). Does this characterize the accuracy available to the builders (±0.3°)?
It is interesting that the lower section of the N. face is almost flat (the difference between lower and upper parts is only 12').
Now consider the hypotheses about why the lower section has such angle of slope.
Stellar.
1. The altitude of the star culminating in the south:
a) Betelgeuse at an altitude of 54° 30' in 2630 BC (Chris Tedder).
b) I have my own hypothesis about which I will write later.
2. The altitude of the star culminating in the north: no candidates.
Geometric.
1. Petrie and Dorner suggest that the design is based on a ratio of 10 : 7 (height : base) which gives a theoretical angle of slope of 55° 00' 29''. This value is very close to the observed average angle for the lower part of the lower section (Petrie's 55° 01'; see table).
2. Legon suggests that the design is based on a ratio of rt2 : 1 (height : base), which gives a theoretical angle of slope of 54° 44' 06''. This value is very close to the observed average angle for the lower and upper parts of the lower section (Petrie's 54° 46'; see table).
The following observation is in favor of the Legon's hypothesis.
Three designs of the Snofru pyramids in Dahshur:
- Bent inner pyramid (Base = 300c; Angle = 60°; Height = 300/2 * tan (60°) = 260c);
- Bent lower section (Base = 362c; Angle = 54° 44' 06''; Height = 362/2 * tan (54° 44' 06'') = 256c);
- Red pyramid (Base = 418c; Angle = 45°; Height = 418/2 * tan (45°) = 209c)
linked by angles (alpha, beta, gamma) as follows:
[drawing by M.Ramirez - The Great pyramid of Giza, an optimized geometry?]
[alpha, beta, gamma are calculated for y,x]
That is, if we accept that the Red Pyramid was planned with the angle of slope of 45° (as Dorner suggests), then not only the angle of inclination of its faces (45,000°) is equal to the angle of inclination of the edges of the Bent pyramid (45,003°), but the angle of the triangular faces of Red pyramid (54,736°) is equal to the angle of slope of the Bent pyramid (54,738° = 54° 44' 17'').
Alex.
Edited 6 time(s). Last edit at 03/09/2020 05:14PM by keeperzz.