Part of a massive, 27km- (16-mile) long defense system, this 4th-century-b.c. fortress is surrounded by three trenches, connected by underground tunnels. These supposedly impregnable defenses were never put to the test: Siracusa fell to the Romans in 212 b.c. without a fight, because the entire garrison was celebrating the feast of Aphrodite. It was here, legend has it, that the Greek mathematician Archimedes famously cried “Eureka!” having discovered the law of water displacement while taking a bath. The evocative ruin overlooking the Siracusan plain is the best-preserved Greek castle in the Mediterranean. The defenses are at the far end of the archaeological zone, about 5km (3 miles) outside the city center near a village called Belvedere; buses 25 and 26 pass the entrance.