Saturday, September 17, 2005

Archimedes (c.290/280 BC - 212/211 BC)

Archimedes was born and mainly lived in Syracuse on the eastern coast of Sicily. He is believed to have been close to Hieron II, King of Syracuse, who tried to encourage Archimedes to use his extraordinary talents for practical purposes. The King had commissioned a gold wreath that he wished to consecrate to the gods. When the wreath was delivered, it weighed the correct amount for which he had been charged. However, he was concerned that some of the gold had been replaced by an equal weight of a metal of lesser value, such as silver or lead. Because of its consecrated nature, dissection or analysis was impossible.
Archimedes was presumably pondering this quandary while visiting the public baths in Syracuse. As he sank into the bath, water overflowed: the further he sank, the more water poured out. Upon realising that the amount of water displaced was a direct measure of his volume, legend has it that he leapt from the bath and ran, naked and dripping, to the King, repeatedly shouting 'Eureka' (I have found it). He knew that if he immersed the crown in water and measured the overflow, he could find its volume. Whatever its shape, if the crown were pure gold it should have an equal volume to an equal weight of pure gold, whatever shape that had. When Archimedes measured the volume of the crown it was greater than the volume of a kilo of gold, and Hieron saw that he had been cheated.
He then gave Archimedes the challenge of launching the Syracusia, an enormous ship weighing 4 200 tons that had been built as a gift for Ptolemy, King of Egypt and which was so heavy that all previous launch attempts had failed. According to Plutarch, Archimedes used a polypaston, or block and tackle, with a large number of sheaves. This effectively created many ropes, with the weight of the ship divided between them. Consequently each rope, including the final rope that was being pulled, had only to support a fraction of the weight: a force of only a fraction of the weight was sufficient to lift the weight. Archimedes realised that with a perfect lever there was no theoretical limit to how large a load could be shifted with any given weight.
Apart from an account of his elegant planetariums, he wrote down nothing other than mathematics. This work included an early approximation of the value for pi, the calculation of relative volumes of spheres and cylinders, and an original system of notation (with a base-value of 100 million) to express enormous numbers. He was also an outstanding astronomer, and invented 'Archimedes' Screw', a device for raising water.
When the Romans invaded Syracuse in 214 BC, Archimedes invented 'engines of war' to defend the city, including cranes to drop rocks, claws to lift ships from the water, and machines to fire missiles. Most famous were the burning mirrors, with which Archimedes is supposed to have set ships on fire. This was theoretically straightforward: a parabolic mirror could be used to focus the rays of the sun onto one point, which would then reach temperatures sufficient to set alight anything at its focal point. The construction was more complicated, and Archimedes possibly approximated a parabolic mirror with a large number of small mirrors: the more mirrors, the closer the approximation.
The siege of Syracuse was, however, to cost him his life. He was reportedly absorbed in his mathematics when captured. Instructions that he be kept alive were ignored when he ordered the Roman soldier to stay away from his work, and he was killed immediately.


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