Final answer:
Greek culture spread to new areas through colonization and conquest, leading to the establishment of Greek-influenced cities across the Mediterranean and Near East, including new centers of Hellenic culture such as Pergamon, Antioch, and Alexandria, as well as widespread Greek settlements in regions like Magna Graecia.
Step-by-step explanation:
The conquests of the Ancient Greeks, particularly during the Hellenistic period after Alexander the Great, vastly extended the reach of Greek culture and influence. Through a mixture of colonization, trade, and military conquests, Greek culture spread far beyond the traditional boundaries of the Greek city-states, affecting regions across the Mediterranean, the Near East, and parts of Central Asia. New centers of Hellenic culture developed in cities such as Pergamon, Antioch, and Alexandria, creating a rich cultural blend of Greek and local traditions. Colonization during the Archaic period led to Greek settlements as far as Spain, the coast of the Black Sea, North Africa, Libya (Cyrene), southern Gaul (Massalia/Marseille), and the large Greek presence in Magna Graecia (southern Italy and Sicily). Additionally, the Greeks maintained an influential presence in the conquered Persian cities and saw their ideas and governance styles merge with local customs.