Much like the Pythagoreans, the Greeks became very interested in the Golden Ratio and the way it showed up in relationships between all sorts of numbers. They experimented with constructions of triangles and rectangles, and they also took the principle a step farther.

     Plato, one of the most well known Greek philosophers theorised about the Golden Ratio. He felt that if a line was divided into two unequal segments so that the smaller segment was related to the larger in the same way that the larger segment was related to the whole, what would result would be a special proportional relationship, which would have special properties. Euclid also discussed this special proportion, although he never gave it any numerical value. As advanced in mathematics as the Greeks were, they had a poor system of numbers and had no zero.

     Despite the poor number system and no standard of measurement, the Greeks put the Golden Ratio to work. Its use in architecture became wide spread, and when Iktinos designed the Parthenon in the 5th century B.C., he used the Golden Ratio throughout it.

The Parthenon

http://www.indiana.edu/~kglowack/athens/ Complete photo credits