The ruined cities of Mashonaland: Being a record of excavation and exploration in 1891

by J. Theodore Bent

At Matindela the only regularly curved piece of wall is that about the principal doorway, but it is so rough in its construction that one hesitates to deal with it, and we can only say that it seems to be built on a curve of 107⅘ feet radius = twice 17·17 × 3·14. The whole appearance of this wall and the slight inaccuracies in the orientation of the decorations which it carries, suggest that it is a more recent wall built roughly as a copy of an original wall on the same foundation.

The ruin at the Lundi River is circular in form and well built, and its diameter is fifty-four feet, which is equal to 17·17 × 3·14.

Of course all the above measurements refer to the outside of the walls at the base, as this is the way in which the tower itself was measured.

The same principle of measurement applies to the curves which determine the shape of the two towers themselves, and this explains why it is that the little tower tapers much more rapidly towards the top than does the great one. If we describe a circular curve with its centre on the same level as the base [[157]]of the great tower and its radius equal to twice 17·17 x 3·14 on 107⅘ feet, we find that it exactly fits the outline of the great tower as it is shown in our photographs. Also, a curve described in a similar way but with a radius equal to twice the diameter of the little tower multiplied by 3·14 (5·45 × 3·14 × 2 = 34·34 feet) will correspond to the outline of that tower.

The towers when built were doubtless made complete in their mathematical form and were carried up to a point as we see in a coin of Byblos, where we have a similar tower represented with curved outlines. Their heights as determined by these curves would be 42·3 and 13·5 feet respectively, and these numbers also bear the same relation to each other that the circumference of a circle does to its diameter.

We have no explanation to give of the position of the little tower relatively to the great one, but there probably was some meaning in it which might appear had we a plan of the original walls around the towers. It is very doubtful that these walls, which now mark off the sacred enclosure, are of the same period as the towers. They are shaded darkly in our plan because they are fairly well built; but although they are better built than most of the secondary walls, yet they are not equal in point of execution to the great outer wall and the towers, and their lines, too, are not so regular as those of the original walls generally are. It seems probable that they are rough copies of some old walls which had fallen, and are wanting in some [[158]]of the essential features of their originals. We can only say that the centre of one tower is distant 17·17 feet from the centre of the other, within a limit of error of two inches.

The angular height of both the towers measured from the centres of the curves which determine their forms is the same—namely 23° 1′.

None of the angular values of the arcs seem to have been of any special significance, except perhaps the angle at the altar in the great temple, which is subtended by the arc AK. The value of this angle is about 57°, and is equal to our modern unit of the circular measure of an angle, which is the angle at the centre of any circle that is subtended by an arc equal to the radius. It is hardly likely that it can have had this meaning to the builders of the temple, and the probable cause of the coincidence is that at A they meant to halve the angular distance between K and the doorway. Besides, the sun’s rays, when it rises at the summer solstice, do not fall directly on the part of the wall beyond A, and this probably had some connection with their reason for changing the radius of the arc at this point.

There is no evidence that any of the trigonometrical functions were known to the builders of Zimbabwe; not even the chord, which was probably the earliest recognised function of an angle, for the chords of the various arcs bear no simple relation to each other. The only interesting mathematical fact which seems to have been embodied in the architecture [[159]]of the temples is the ratio of diameter to circumference, and it may have had an occult significance in the peculiar form of nature worship which was practised there. We do not suppose that it was intended to symbolise anything of an astronomical nature, and it is extremely improbable that the builders of Zimbabwe had any notion of mathematical astronomy, for their astronomy was purely empirical, and amounted merely to an observation of the more obvious motions of the heavenly bodies. When the minds of men were first interested in geometry it would at once occur to them that there must be some constant ratio between the circumference of a circle and its diameter, and they would easily discover what this ratio was, and they may have considered this discovery so important and significant that they desired to express it in their architecture. Analogous instances of an embodiment of simple mathematical principles in architectural forms will occur to every one.

The centres of the arcs seem generally to have been important points, and altars were sometimes erected at them from which the culminations or meridian transits of stars could be observed, and on which sacrifices were probably offered to the sun when it was rising or setting at either of the solstices.