Issue No.3 Sept/Dec 1983

Life of a Mathematician - ARCHIMEDES

by Edmund Cannon

Archimedes was born in Syracuse, the Greek colony on Sicily. He spent most of his time there but did study for a while under a former pupil of Euclid in Alexandria.

The most famous story about Archimedes is that Heiron II (ruler of Syracuse) wanted to find if a crown was pure gold. While taking a bath, Archimedes realised that his body was displacing water. If the crown and a piece of gold weighed the same amount and displaced the same amount of water, then the crown would be pure gold. Archimedes is reported to have run round the streets, still naked from his bath, shouting 'Eureka' (I've got it). Archimedes' success was the goldmaker's downfall and cause of execution, for the crown contained base metals. Carrying this idea further, Archimedes discovered up-thust, the upward push in water equivalent to the weight of water displaced. e.g. a metal bar will sink, yet a boat made of metal will float as its displacement in water is equal to its overall weight.

Archimedes also found 'PI' to greater accuracy than ever before in "Measurement of the Circle" (one of his surviving treatises). 2000 years before the discovery of differential nucleus by Isaac Newton.

Archimedes discovered the way levers could be used to increase one's lifting capability, at the expense of moving it further. He once boasted to his friends, "Give me a place to stand and I'll lever the world."

His final years were spent helping to defend Syracuse from the Romans. During the siege, cranes that could overturn ships were reported by the Romans. Archimedes is also credited with the invention of the catapult. In 212 BC, Syracuse fell to the Romans. Their commander Marcellus ordered Archimedes to be brought to him,not killed during the pillaging of the city. Archimedes refused to meet Marcellus immediately as he was working on a mathematical problem and so a Roman killed him.

E. Cannon