Archimedes is supposed to have run naked through Syracuse shouting *Eureka!* — 'I have found it!' — after a sudden insight came to him while bathing. What had he figured out?
King Hiero II had commissioned a gold crown but suspected the goldsmith of substituting some silver. Archimedes realised in the bath that an object's volume could be measured by the water it displaces — and that comparing the displacement of the crown with that of a pure-gold reference of the same weight would reveal the fraud. The story comes from Vitruvius (writing about 250 years later) and may be embellished. The Eureka technique is now substantially recognised as a real Archimedean principle (the law of buoyancy), independently developed in his treatise *On Floating Bodies*. The mirror/burning-glass war machine is a separate (and probably apocryphal) story from the siege of Syracuse.
Read the full story →He used balance points to discover the volumes of curved solids, then proved them with strict geometry. The Greeks called it forbidden. He called it the Method.
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