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Interestingly, a second inscription found 30 courses of stones higher is
dated 2 to 4 years later than the inscription found at the base. This gives an
idea about the speed at which the Egyptians were able to build a monument like
this pyramid. Within four years, 30 percent of the pyramid had been
completed, and the entire pyramid was finished in about seventeen years.
There is little doubt that Snofru was finally buried in this pyramid,
although the fragments of human remains found inside the burial chamber are not
certain to have been his. Interestingly, during the reign of Pepi I of the 6th Dynasty, this pyramid
along with its southern neighbor, the Bent Pyramid, was considered as one
estate.
The Geometry of the Red Pyramid
The Red Pyramid was built with a slope of only 43°22'.
Its base length is 220 meters, that is 32 meters more than the Bent Pyramid.
Its height is the same as the Bent Pyramid.
Basic Dimensions:
- base length: 220 m
- slope: 43o 22'
- height: 104 m
- burial chamber: 4.18 x 8.55 m (height: 14.67 m)
Fig. 2
The Red Pyramid and its internal structure.
Source: Lehner, Complete Pyramids, p. 104-105.
The broader base and lower slope were intended to better spread the mass of
this pyramid and thus avoid the structural problems that had temporarily halted
works on the Bent Pyramid.
The internal structure of this pyramid is a further continuation of the
pyramid at Meidum and the Bent Pyramid. Contrary to this latter monument,
however, there is only one internal structure, making it a lot more simple.
The entrance is located 28 m high up in the Northern face of the pyramid.
A
descending passage (at an angle of 27 degrees) leads down for 62.63 m to a short horizontal corridor
7.4m long.
This is followed by two almost identical antechambers with corbelled roofs. Both
antechambers measure 3.65 by 8.36 m and are 12.31 m high.
The burial chamber can only be reached via a short passage which opens high
up in the wall of the second antechamber. The burial chamber measures 4.18 by
8.55 m. Its corbelled roof goes up to a height of 14.67 m. It is
located well above ground level, in the core of the pyramid.
The chapel built against the Eastern face of the pyramid was finished
hastily, probably after the death of Snofru. It is somewhat more elaborate than
the eastern chapel of the Red Pyramid or the pyramid at Meidum in that it houses
an inner sanctuary, flanked by two smaller chapels.
There is no trace of a causeway leading down to the Valley Temple, of which
few remains were found at the end of the 19th century.
In fact, all three of the chambers in this pyramid have corbelled ceilings,
with between eleven and fourteen layers. Even with some two million tones of
stone above, this ceiling design is so strong that there are no cracks or
structural problems even today.
Fig. 3
The Red Pyramid, Corbelled Ceiling
A short passage on the south side of the first chamber leads to
a second chamber. These first two chambers are at ground level, while a third
chamber is higher, built within the masonry of the pyramid itself.
The second chamber is unusual in that it lies directly under the
apex of the pyramid, or center point of the pyramid. It is one of the only
pyramids in Egypt to have this design layout. The final chamber, with its
entrance passageway about 25 feet above the floor of the second chamber, can be
accessed by a staircase (of modern construction).
Egyptologists believe the final chamber was intended to be the actual burial
chamber. The floor has been excavated in an
unsuccessful attempt to find other passageways.
Design of the Red Pyramid
It appears that the Red Pyramid design was based on the pentagon.
Each triangular segment of a pentagon has 72° at the central point (360°/5=72°).
Using 4 of the 5 triangles of a pentagon a pyramid can be made
(with a base equal to the
base of the pentagon's side)
that will have the same proportions as the Red
Pyramid.
Fig. 4a
The pentagon and the red pyramid - perspective view.
© 2004 by World-Mysteries.com
Fig. 4b
The pentagon and the red pyramid - top view.
© 2004 by World-Mysteries.com
Using very basic reasoning we can see that the
angle of the slope of the pyramid
(α ) can be found from this equation cos α
= tan 36°, which gives α= 43°24'.
This theoretical slope angle of 43°24' ( 43.402680°) is practically identical
to the measured slope angle of the Red Pyramid: 43° 22'.
* * *
Two slope angles of the Bent Pyramid match a design based on a HEXAGON
(for the lower part)
and a PENTAGON (for the upper part) principles:
|
The Bent Pyramid -
slope angle: |
Measured |
Theoretical |
|
Lower
part |
54°
27' |
54°
44' |
|
Upper
part |
43°
22' |
43°
24' |
Note: For hexagon: cos α
= tan 30° --> α= 54° 44'
Fig. 5 The Bent Pyramid
Fig. 6
The hexagon principle gives the slope angle
for the base of the Bent Pyramid.
© 2004 by World-Mysteries.com
Image Source:
http://www.invisibletemple.com/geometry1.html
Enter the Bent Pyramid! ****/****
* * *
For the angle of the Great Pyramid, any theory of the base, combined with any
theory of the height, yields a theoretic angle; but the angles actually proposed
are the following (Source: Page 184, The Pyramids and Temples of Gizeh by
Sir W.M.Flinders Petrie 1883):
|
Angle of casing measured
By theory of 34 slope to 21 base
Height : circumference :: radius to circle
9 height on 10 base diagonally
7 height to 22 circumference
area of face = area of height squared
(or sine) = cotangent, and many other relations)
2 height vertical to 3 height diagonal
5 height on 4 base |
51º 52' ± 2' (51.867)
51º 51' 20"
51º 51' 14.3"
51º 50' 39.1"
51º 50' 34.0"
51º 49' 38.3"
51º 40' 16.2"
51º 20' 25" |
Fig. 7 The Great Pyramid design
principle
Related link:
Geometry of the Great Pyramid
|
When ancient architects completed construction on
the Great Pyramid at Giza, they left behind the greatest riddle of the
engineering world how did builders lift limestone blocks weighing an average
of two and a half tons, 480 feet up onto the top of the pyramid? For
centuries, adventurers and Egyptologists have crawled through every passageway
and chamber of the Great Pyramid, measuring and collecting data in an attempt
to determine how it was built. For the first time, a revolutionary theory
argues that the answer may be inside the pyramid. Architect Jean-Pierre Houdin
has devoted his life to solving this mystery by creating incredibly accurate
blueprints of the Great Pyramid, using cutting-edge 3-D software. Unlocking
the Great Pyramid follows Houdin and renowned Egyptologist Bob Brier in Giza
as they put Houdins theory to the test.
Related Book:
The Secret of the Great Pyramid: How One Man's Obsession Led to the Solution
of Ancient Egypt's Greatest Mystery (Hardcover) by Bob Brier (Author),
Jean-pierre Houdin (Author) -- Oct 2008
|
 |
|
Based on the author's work in Egypt in the 1880s,
this unusual volume addresses one of history's greatest puzzles -how were the
pyramids of Gizeh built? Before Petrie undertook this study, the Great Pyramid
was a byword for paradox - something that was generally familiar, yet not
accurately known. No measurements or detailed examination had been performed.
Petrie set out to apply mathematical methods to the study of the pyramids and
surrounding temples, with the objective of understanding the methods and
abilities of the ancient workers. The result, presented in this volume, is
a complete set of measurements of the pyramids, both inside and outside.
These provide the foundation for the rest of the book, which deals with the
architectural ideas of the pyramid builders, the mechanical methods they used,
and a comparison of previous theories with the facts that Petrie had newly
established.
Another Edition:
Petrie, W. M. F. The
Pyramids and Temples of Gizeh. London. 1883
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More Subject Related Books
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