Archimedes died tragically during an invasion of Syracuse at the hands of a soldier who was ordered by his superior to spare him.  At the time, Archimedes was intent on working out some problem with a diagram.  According to historians, Archimedes played an important role in defending the city.  He designed ballistics machines that hurled rocks at ships and cranes that dropped large stones on them.  I read several stories of a great lever lifting them out of the water.  This illustration is a painting based on the tale of Archimedes' claw.

The exact circumstances of his death differ in report.  Archimedes requested that his tombstone display a cylinder containing the largest possible sphere and inscribed with the ratio of the cylinder's volume to that of the sphere. Archimedes considered the discovery of this ratio his greatest of accomplishment.