User:Dave Light/Circular

Protective Circular Symbolism in Egyptian Tomb Architecture
NOTE - THIS ARTICLE IS UNDER CONSTRUCTION AND IS NOT INTENDED FOR PUBLICATION AT PRESENT

The shen ring and cartouche were symbols that represented eternal protection for the pharaoh, and all that the pharaoh ruled.

The shen represented a symbolic protective perimeter around the pharaoh and the concept was incorporated into the tomb, palace and temple designs to form a protective perimeter around the pharaoh's royal buildings.

This apotropaic symbolism was incorporated into Egyptian tomb architecture through the use of artistic representations painted on the walls, the use of chambers in the form of cartouches, the use of chambers and tombs with dimensioned proportions based on the circle and by way of texts expressing the concepts in question. The symbolism was perhaps most simply expressed iconographically by the painting of the shen ring directly on the walls of tomb chambers and the sarcophagi, and represented eternal protection for the pharaoh. In later times this protection was extended to non royal nobles. The symbolism was also extended to protecting the hieroglyphs spelling out the pharaoh's name, when in the form of the cartouche (which is an extended circular shen ring). Most impressively, it was extended to the layout of the pyramids of the Giza necropolis, as well as to the royal tombs in the valley of the kings.

Protective symbolism for the perimeter of important tombs, compounds and temples seems to have been applied on a wide basis, and many important ceremonial rituals concerning perimeters were associated with the god Horus, as well as the shen and cartouche. Horus is often shown holding the shen ring, often above the pharaoh himself, or standing on top of the serekh symbol which represented the pharaoh's name as well as the pharaoh's temple or palace. The serekh tradition seems to have started around dynasty 0, whereas the shen and cartouche iconography began during the third dynasty. These symbols are clearly shown in the Heb Sed festival frescoes on the walls of the subteranean chambers of the Stepped Pyramid of Djoser.

The ideology may have been primarily symbolic, but the circular proportions may also have been thought to bestow structural strength. Analyses of the mathematic curve sketched on the 'saqqara ostracon' for example have suggested that while the form is close to being catenary it is in fact based on a circular segment. This sort of association between circles and structural strength may have been of interest to 3rd and 4th dynasty architects who were struggling with structural engineering problems. Several of the pyramid from the Old Kingdom suffered from structural problems, some even developing during the construction process itself. Even the giant apexed relieving spaces above the burial chamber in Khufu's great pyramid could not protect the granite roof beams from cracking, although they have remained in place for 45 centuries.

In the Valley of the Kings, several of the royal tomb chambers were designed in a cartouche shape, such as KV34 and KV42, and this feature was echoed in the shapes of the sarcophagi, often either cartouche shaped such as that in KV8 (Merenptah), KV34 (Thuthmosis III), and KV11 (Ramesses III - sarcophagus now in the Louvre, lid in Fitzwilliam Museum Cambridge) or having shens drawn at the ends, most usually held by Isis (feet) and Nephthys (head).

Since the Old Kingdom, sarcophagi echoed the architectural forms of royal temples and tombs, most notably with respect to the well known Palace Facade design. In later anthropomorphic sarcophagi the palace facade motif was dropped, and the shen ring, often held by Horus, was painted onto the exteriors and interiors of the coffin.

As can be seen from the early serekhs with Horus and the palace facade, the pharaoh was almost synonymous with the palace, and perhaps used this comparison to legitimise his rule. From the time of Akhenaten the word pharaoh was used. This originally meant great house - pr-Aa - and came to refer to the king over time.

The tomb itself was originally called the castle or house of millions of years.

From architectural texts from later antiquity we find confirmation from the works of Vitruvius in de Architecture, Book III, Chapter 1, 1:

"The design of Temples depends on symmetry, the rules of which Architects should be most careful to observe. Symmetry arises from proportion, which the Greeks call ἀναλογία. Proportion is a due adjustment of the size of the different parts to each other and to the whole; on this proper adjustment symmetry depends. Hence no building can be said to be well designed which wants symmetry and proportion."

book VI, chapter 3, 3 that the length and breadth and proportions of the courts or atria of temples was considered of importance. He writes "The length and breadth of courts (atria) are regulated in three ways. The first is, when the length is divided into five parts, and three of them are given to the width. The second, when it is divided into three parts, and two are given to the width. The third is, when a square being described whose side is equal to the width, a diagonal line is drawn therein, the length of which is to be equal to the length of the atrium"

of measured slopes was therefore expressed as the number of palms and digits moved horizontally for each cubit rise.

One of the most widely known applications of the seked slope measurement system was in the construction of the pyramids of Egypt. Although there is no direct evidence of its application from the archaeology of the Old Kingdom, there are examples from mathematical papyrii dating to the Middle Kingdom that show the use of this system for defining the slopes of the sides of pyramids, based on their height and base dimensions. The most widely quoted example is perhaps problem 56 from the Rhind papyrus.

The most famous of all the pyramids of Egypt is the Great Pyramid of Giza built around 2,550 B.C.. Based on the surveys of this structure that have been carried out by Flinders Petrie and others, the slopes of the faces of this monument were a seked of 5 1/2, or 5 palms and 2 digits [See figure above], which equates to a slope of 51.84º from the horizontal, using the modern 360 degree system. This slope would probably have been accurately applied during construction by way of 'A frame' shaped wooden tools with plumb bobs, marked to the correct incline, so that slopes could be measured out and checked efficiently.

Furthermore, according to Flinders Petrie's survey data in "The Pyramids and Temples of Gizeh" the mean slope of the Great Pyramid's entrance passage is 26º 31' 23" ± 5". This is less than 1/20th of one degree in deviation from an ideal slope of 1 in 2, which is 26º 33' 54".

This equates to a seked of 14, and is generally considered to have been the intentional designed slope applied by the Old Kingdom builders for internal passages.

Pyramid Slopes




Many of the smaller pyramids in Egypt have varying slopes, however, like the Great Pyramid of Giza, the pyramid at Meidum is thought to have had sides that sloped by 51.842º or 51º 50' 35"

The Great Pyramid scholar Professor I.E.S Edwards considered this to have been the 'normal' or most typical slope choice for pyramids. Flinders Petrie also noted the similarity of the slope of this pyramid to that of the Great Pyramid at Giza, and both Egyptologists considered it to have been a deliberate choice, based on a desire to ensure that the circuit of the base of the pyramids precisely equalled the length of a circle that would be swept out if the pyramid's height were used as a radius. Petrie wrote "...these relations of areas and of circular ratio are so systematic that we should grant that they were in the builder's design".

The seked of a pyramid is described by Richard Gillings in his book 'Mathematics in the Time of the Pharaohs' as follows:

"The seked of a right pyramid is the inclination of any one of the four triangular faces to the horizontal plane of its base, and is measured as so many horizontal units per one vertical unit rise. It is thus a measure equivalent to our modern cotangent of the angle of slope. In general, the seked of a pyramid is a kind of fraction, given as so many palms horizontally for each cubit of vertically, where 7 palm equal one cubit. The Egyptian word 'seked' is thus related to our modern word 'gradient'."

External References

 * Meidum: Site of the Broken Pyramid & Remnants of the First True Pyramid- Virtual-Egypt
 * 'The Pyramids and Temples of Gizeh' online: Petrie's 1882/3 survey of Giza