Archimedes

Studied the principles of buoyancy and the lever, and designed defensive machines during a siege.

Life

Scholar of Syracuse

Archimedes was born in Syracuse, a Greek city-state on Sicily; his father was an astronomer. In his youth he went to study in Alexandria and had close contacts with the school of Euclid. Syracuse was then a wealthy city at the western edge of the Hellenistic world and also on the front line of the struggle between Rome and Carthage for Sicily.

Mathematics and City Defense

In mathematics he calculated upper and lower bounds for pi and found the ratio of the volumes of a sphere and a cylinder; the principle of buoyancy reportedly came to him in a bathtub as he worked out how to detect an adulterated crown, and he leapt out of the bath crying "Eureka!" When Rome besieged Syracuse in 214 BCE, he designed catapults, ship-seizing claw cranes and other machines to help defend the city, so that the Roman army long failed to take it.

Killed when the city fell

When the city fell in 212 BCE, legend has it that he was working out a geometric figure in a sand tray and was killed for ignoring a Roman soldier's shouts, even though the commander Marcellus had ordered his life spared. His deathbed words "my circles" and the story of his bathtub insight are widely told, but both come from later biographies, and whether they really happened is hard to confirm.

Legacy

Archimedes is widely regarded as one of the greatest mathematicians and engineers of antiquity; he used the method of exhaustion to find areas and volumes, an approach close to later integral calculus, and in physics he laid the foundations of statics and hydrostatics. His works circulated again during the Renaissance and deeply influenced Galileo Galilei and others. However, legends such as his "focusing sunlight with mirrors to burn enemy ships" mostly come from accounts written centuries later, and modern experiments still dispute their feasibility.

Major works & achievements

• Proved that the volume of a sphere is two-thirds that of its circumscribed cylinder
• Determined that pi lies between 3.1408 and 3.1429
• Formulated the principles of buoyancy and the lever
• On Floating Bodies, Measurement of a Circle, The Sand Reckoner and others

Did you know? He wished to have his tombstone carved with a sphere inscribed in a cylinder; Cicero found the tomb while serving in Sicily.

Key dates

• 287 BCEBorn in Syracuse
• 250 BCEStudied the lever and the principle of buoyancy
• 240 BCEInvented the Archimedes screw water pump
• 214 BCERome besieged Syracuse; he designed defensive machines
• 212 BCEKilled when the city fell