When the Greeks were at their height, they did not know of the arch, or did not employ it in their religious buildings. So they used post and lintel constuction, which are posts or pillars with a flat piece of stone or wood between, which is the lintel. They did not re-inforce with metal, or very rarely, since metal of all kinds was scarce and expensive and mainly used for small items like tools and weapons.
Stone is strong in compression but weak in tension. The undersurface of the lintel between columns is in tension and if the distance between columns is too great the stone will break from the bottom up.
This meant that temples were a forest of columns supporting the lintels, which in turn supported the roof. The roof was a gable, that is, triangular at two ends with a ridge between, because this sheds rain water easily. A flat roof is always more likely to leak, even today.
The ancient Egyptians built the same way, but used flat roofs since rain was all but unknown in Egypt.
Columns were decorated near the tops in three ways, Doric, Ionic and Corinthian. I forget the difference between Doric and Ionic, but the Corinthian was decorated near the top using a pattern based on the leaves of the acanthus plant. The capitals were based on the wood blocks once used to spread the load on wooden columns and the stone temples were ultimately based on wooden buildings.
The proportions were chosen carefully according to what was most pleasing to the eye. This turns out to be related to the Golden Ratio, which they were perfectly capable of calculating quite accurately.
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