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Designs in The Tomb of Tausert and Setnakht

In the Valley of the Kings are other examples of the design work of the ancient Egyptian Geometricians. For five hundred years, from about 1500 to 1000 BC, the period when Moses led the people of Israel out of Egypt, down to the time of the establishment of the kingdom under King David, the Pharaohs were preparing tombs for themselves in the valley. The site is ideal on several grounds. A thick layer of fine white limestone lies underneath the hills, but readily accessible for the carving of tombs. The valley is near the Nile river, which could be used to carry the embalmed bodies from the royal palaces along the river. The area could be easily guarded because the isolated geography was surrounded by hills that offered convenient visual vantage points. Remains of some of the ancient guard sites still exist.

The tomb of Tausert and Setnakht, numbered by Egyptologists as KV 14, has two burial chambers, intended respectively for the Queen and the King. The chambers have vaulted ceilings, similar to those of Ramesses VI, with the ends decorated in geometric designs. The designs follow simple mathematical principles.

 The first chamber, J1, was finished; it measured 10 cubits wide and 20 cubits long. The second chamber, J2, was never finished; hence it does not contain designs that we can investigate for geometric properties. The width of J2 was 12 cubits; the length was 25 cubits. These measures were obtained from the published figures of the Theban Mapping Project.

Here is one end of the chamber numbered J1 by the designers of the Theban Mapping Project.

The large image of a animal headed bird was the Sun God, the main figure of the design.

The shape of the vault was a geometric ellipse. On the end shown are two triangles that enclose a square in the top center of the design. The levels of the respective panels are all geometrically related to the design.

We can see human figures engaged in various sacred activities in all of the panels. At the bottom is a boat intended to convey the Queen to heaven.

I used QuickCad software to determine the shapes and measures of the several design elements. The following shows the measures of these elements. While the actual painted design was rough, the measures were held sufficiently close to determine the design intent.

The ellipse which composed the vaulted arch had a ratio of 5:4, 10 cubits wide, the width of the chamber, and eight cubits high. The chord which defined the beginning of the vault and the top panel was one cubit above the major axis of the ellipse. We can see how the arch was indented slightly from the full chamber width. The bottom of the second panel containing the image of the Sun God was 1.5 cubits below the major axis. The bottom of the lowest panel was 3.5 cubits below the major axis.

Below is the design of the top panel.

I show design lines similar to those that must have been used by the architect. The center is three cubits square with the top of the square drawn tangent to the top of the ellipse. The two triangles are each two cubits wide to form a 3:2 ratio. (This ratio is used as the slope of the entrance passage of the Giza I pyramid.) The tops of the triangles and the square are cut off by the arch of the ceiling. The two outside distances from the bottom of the triangles to the end of the chord are not quite 1.5 cubits because the arch limits their reach.

We can readily see how the ellipse was familiar to this period in Egyptian history, and could be designed in different ratios.

 

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