When I was eight I remember looking at pictures of stereotypical ancient Greeks in a children's text book. The teacher told us that it was no coincidence if we thought they resembled Romans (who we'd "leaned" about some months before) because the Romans copied there entire culture from the Greeks
The Romans did adopt some areas of Greek culture, many Greeks were taken as slaves and served as teachers and doctors in households, however the Romans admired the Greeks of around the 4th century BC as great heroes and legends whilst they considered the Greeks that were around in their time to be little more than a warrior race of barbarians, and hence a threat to the Roman way of life
Benjamin Isaac, Invention of Racism in Classical Antiquity (Princeton: Princeton University Press, 2004)