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 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. Around the outside of the wall of the great temple, between the points marked A and B on plan, there extend two bands of a kind of chevron pattern, formed, as will be seen from the illustrations, by placing stones on their edges. This pattern seems to have been symbolical of fertility, and it extends along the part of the wall which receives directly the rays of the sun when rising at the summer solstice. It reminds one of the Egyptian hieroglyphic symbol for water, and of how naturally the idea of water would be associated with fertility in the mind of a solar worshipper. It also resembles the symbol for the zodiacal sign of Aquarius, and we might suppose that the temple was built when the sun was in this sign of the zodiac at the summer solstice, did such a supposition not carry us back to too remote a period. Besides, the sun is generally believed to have been in Capricornus at the December solstice at the period at which the zodiac was invented, and when its signs received their names.