Archimedes was born around 287 BC in Syracuse, the great Greek colony in Sicily, son of the astronomer Phidias. He probably studied in Alexandria, the scientific centre of the Hellenistic age, and stayed in touch with scholars of the Museum such as Eratosthenes. He lived at the court of King Hiero II, perhaps a relative.
Eureka!
According to Vitruvius, Hiero had a gold crown made and suspected the goldsmith of mixing in silver. He asked Archimedes to find out without damaging the crown. Getting into his bath, Archimedes saw the water rise: he realised a submerged body displaces a volume of water equal to its own. He ran naked into the street shouting "Eureka!", "I have found it!". Comparing the water displaced by the crown and by a block of gold of the same weight, he exposed the fraud.
Great discoveries
| Discovery | What it is |
|---|---|
| Archimedes' principle | A body immersed in a fluid is pushed upwards by a force equal to the weight of fluid displaced |
| Law of the lever | Weights and distances from the fulcrum are inversely proportional: "Give me a place to stand and I will move the earth" |
| Pi | He showed π lies between 3 10/71 and 3 1/7, using 96-sided polygons inside and outside a circle |
| Sphere and cylinder | A sphere's volume is two-thirds that of the cylinder containing it: so proud was he that he wanted it carved on his tomb |
| Area of the parabola | Used a method anticipating integral calculus |
| The Sand Reckoner | Calculated how many grains of sand the universe could hold, inventing a system for writing huge numbers |
Machines
Archimedes was also a brilliant engineer. The Archimedes screw, a cylinder with an internal spiral that lifts water as it turns, is still used today. He built planetaria reproducing the movements of the heavens and pulley systems with which, it is said, he single-handedly hauled a beached ship.
The siege of Syracuse
In the Second Punic War Syracuse sided with Carthage and in 214 BC was besieged by the Romans under Marcellus. For two years Archimedes' machines kept the enemy at bay: catapults, cranes that grabbed ships and capsized them (the "iron hand") and, according to later writers, burning mirrors focusing the sun on the sails, a story whose plausibility is still debated.
Death
In 212 BC the Romans entered the city during a festival. Archimedes, studying geometric figures drawn in the sand, was killed by a soldier, even though Marcellus had ordered him spared. His last words are said to have been "Do not disturb my circles". A century and a half later Cicero found his neglected tomb, recognising it by the sphere and cylinder.
The palimpsest
In 1906 it was found that a Byzantine prayer book had been written in the 13th century over a scraped-off 10th-century manuscript of Archimedes' works, including The Method, thought lost. Using modern imaging, between 1999 and 2008 much of the hidden text was recovered.
See also Greek science and Pythagoras.