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some of the best opportunities to learn are the moments in which we are perplexed. those moments in which youbegin to wonder and question. these moments have happenedthroughout history. and have led to some trulyamazing discoveries. take this story, for example. there once was a fellow named archimedes. he was born in 287 b.c. in the cityof syracuse in sicily. he was a greek mathematician,physicist, engineer,
inventor, and astronomer. one day, archimedes was summonedby the king of sicily to investigate if he hadbeen cheated by a goldsmith. the king said he had given a goldsmiththe exact amount of gold needed to make a crown. however, when the crown was ready, the kingsuspected that the goldsmith cheated and slipped some silver into the crown, keeping some of the gold for himself. the king asked archimedesto solve the problem.
but there was a catch: he couldn'tdo any damage to the crown. one day, while taking his bath, archimedes noticed that the waterlevel in the bathtub rose and overflowed as he immersedhimself into the tub. he suddenly realized that how muchwater was displaced depended on how muchof his body was immersed. this discovery excited him so muchthat he jumped out of the tub and ran through the streetsnaked, shouting "eureka!" which comes from the ancientgreek meaning "i found it."
what did he find? well, he found a wayto solve the king's problem. you see, archimedes neededto check the crown's density to see if it was the sameas the density of pure gold. density is a measure of an object's massdivided by its volume. pure gold is very dense,while silver is less dense. so if there was silver in the crown, it would beless dense than if it were made of pure gold. but no matter what it was made of,the crown would be the same shape, which means the same volume.
so if archimedes could measurethe mass of the crown first, and then measure its volume, he could find out how dense it was. but it is not easy to measurea crown's volume - it has an irregular shape, that's differentfrom a simple box or ball. you can't measure its size and multiplylike you might for other shapes. the solution, archimedes realized, was to give the crown a bath. by placing it in water and seeinghow much water was displaced,
he could measure the volume, and he'd calculatethe density of the crown. if the crown was lessdense than pure gold, then the goldsmith most definitelycheated the king. when archimedes went backto the king and did his test, the story says, he found that the goldsmithhad indeed cheated the king, and slipped some silver in. these days, using the way an object displaceswater to measure volume is called archimedes' principle. thenext time you take a bath,
you can see archimedes'principle in action, and maybe you'll havea genius idea of your own.