Why did mathematical relations become necessary?
A lot of temples dedicated to Apollo were built in Greece and in the Greek colonies, and they show the spread of the cult of Apollo, and the evolution of the Greek architecture, which was mostly based on the rightness of form, and on mathematical relations. Some of the earliest temples, especially in Crete, don't belong to any Greek order. It seems that the first peripteral temples were rectangle wooden structures. The different wooden elements were considered divine, and their forms were preserved in the marble or stone elements of the temples of Doric order. The Greeks used standard types, because they believed that the world of objects was a series of typical forms which could be represented in several instances. The temples should be canonic, and the architects were trying to achieve the esthetic perfection. From the earliest times there were certain rules strictly observed in rectangular peripteral and prostyle buildings. The first buildings were narrow to hold the roof, and when the dimensions changed, some mathematical relations became necessary, in order to keep the original forms. This probably influenced the theory of numbers of Pythagoras, who believed that behind the appearance of things, there was the permanent principle of mathematics.