Thursday, 2 October 2014

The pyramid of Blood

The Red Pyramid at Dashur has the second largest base of any pyramid in Egypt (only slightly smaller then the Great Pyramid of Khufu at Giza); each side measures 220m (722 feet).  However, with it's sides sloping at 43°22', it is substantially shorter at 104 meters (343 feet). Nevertheless, it is the fourth highest pyramid ever built in Egypt, with almost 160 layers of stone. Stripped from its limestone casing, this pyramid reveals the reddish sandstone used to build most of its core. This explains its modern-day name, the Red Pyramid. Its Ancient Egyptian name was "The Shining One".

The severe structural problems encountered while building the Bent Pyramid South of Dashur, led Snofru (Sneferu) to build yet another pyramid, at a small distance to the North. Significantly, the Red Pyramid was the first successful, true, cased Pyramid built in Egypt, ushering in the era of the Giza style pyramids.
Fig. 1  The Red Pyramid of Snofru (Sneferu) near Dashur
Built by Khufu's father, Snefru, what really makes this pyramid special today is the lack of crowds and circus atmosphere that plagues the Giza Plateau, along with the fact that it can currently be entered without limitation.
Fig. 1b  Pyramids of Dashur (fragment of the panorama).
Click on the link above to view the entire panorama (JPG - 380KB).
Note: Remember to enlarge image if you have
the "automatic image resizing" enabled.
Photo courtesy of Frank Dörnenburg
Tura limestone was used as casing stone to cover the pyramid.  Though some casing still remains, most has been removed.  However, about every twentieth casing stone discovered had inscriptions on the back sides.  Some were inscribed with the cartouche of Snefru while others had inscriptions in red paint naming the various work crews, such as the "Green Gang" or the "Western Gang". Snefru's cartouche was an important discovery, particularly since there are no identifying inscriptions within the pyramid.  
East of the pyramid is what remains of a mortuary temple, as well as the first capstone (Pyramidion) ever found belonging to an Old Kingdom Pyramid. It was recovered in fragments and reconstructed. The mortuary temple itself, though nothing much remains, is significant because Snefru pioneered the east west alignment of Egyptian temples to match the path of the sun.

The Red Pyramid History

The inscriptions found on the back of the casing stones gave us clues to how long the pyramid took to build and also revealed the sequence of work that took place. An inscription found at the base of this pyramid has shown that work had started during the year of the 15th cattle count of Snofru's reign. Since the cattle counts were held at irregular intervals during this reign, this refers to somewhere between Snofru's 15th and 30th year. It is very likely that the pyramid construction was started at the time when structural problems encountered when building the Bent Pyramid forced the builders to temporarily abandon this project.

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
Fig. 4b
The pentagon and the red pyramid - top view.
© 2004 by
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'.

* * *

The Bent Pyramid

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:
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
* * *

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"


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