Archimedes and the Baths: Not only one Eureka

In the light of recent archeological studies of the North Baths at Morgantina, we discuss Archimedes’ treatment of cross vaults and of the unusual cylindrical shape called the ‘hoof’ in his work usually referred to as the Method. Our conclusion is that Archimedes’ study of these solids may have been inspired by some real edifice in the Syracuse of his time. The presumed vaulting in the Hellenistic baths at Syracuse could have provided this inspiration; however, because the archaeological evidence for this presumed vaulting no longer exists, the dome and barrel vaults of the comparable bath complex at Morgantina provide important information that helps to elucidate the approach taken by Archimedes in his exploration of particular shapes. We conclude with the observation that the question of the possible role of Archimedes in the invention of these early domes and vaults must remain open, because of the current lack of relevant documentation.