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The Romans are not famous for their conquests in mathematics so much as they are known for their military conquests. In fact, the Romans' application of the Golden Ratio was not original. Instead, as they conquered Greece, they adopted most of the Greek culture.
However, the Romans advanced the Golden Ratio in their own way. Virgil's Aeneid was analyzed at Princeton during the 1940s, and the proportions of lengths of paragraphs were close to the Golden Ratio. The Roman state extended its influence over most of Europe and Northern Africa for several hundred years, and spread aspects of Greek culture--including architecture--into these areas. Later, when the Roman empire fell to Germanic tribes, ideas and influence continued to be spread into the Middle Ages.
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