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Archimedes: Water
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The most commonly related anecdote about Archimedes tells how he invented a method for measuring the volume of an object with an irregular shape. According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hiero II, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith.[12] Archimedes had to solve the problem without damaging the crown, so he could not melt it down in order to measure its density as a cube, which would have been the simplest solution. While taking a bath, he noticed that the level of the water rose as he got in. He realized that this effect could be used to determine the volume of the crown, and therefore its density after weighing it. The density of the crown would be lower if cheaper and less dense metals had been added. He then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" "I have found it!" (Greek: "εύρηκα!")[13]
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Archimedes’ most famous (though not the greatest) accomplishment was when Hiero became suspicious that a crown made for him by his goldsmith was diluted with silver. Not knowing what to do, he turned to Archimedes for help. Archimedes realized that if there was silver in the crown it would displace more water than would be displaced by gold of an equal weight. As it turned out, the king's fears were justified; the goldsmith had cheated after all.
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