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Some of the best opportunities to learn

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are the moments in which we are perplexed.

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Those moments in which you[br]begin to wonder and question.

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These moments have happened[br]throughout history.

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and have led to some truly[br]amazing discoveries.

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Take this story, for example.

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There once was a fellow named Archimedes.

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He was born in 287 B.C. in the city[br]of Syracuse in Sicily.

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He was a Greek mathematician,[br]physicist, engineer,

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inventor, and astronomer.

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One day, Archimedes was summoned[br]by the king of Sicily

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to investigate if he had[br]been cheated by a goldsmith.

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The king said he had given a goldsmith[br]the exact amount of gold

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needed to make a crown.

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However, when the crown was ready, the king[br]suspected that the goldsmith cheated

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and slipped some silver into the crown,

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keeping some of the gold for himself.

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The king asked Archimedes[br]to solve the problem.

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But there was a catch: he couldn't[br]do any damage to the crown.

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One day, while taking his bath,

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Archimedes noticed that the water[br]level in the bathtub rose

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and overflowed as he immersed[br]himself into the tub.

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He suddenly realized that how much[br]water was displaced

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depended on how much[br]of his body was immersed.

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This discovery excited him so much[br]that he jumped out of the tub

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and ran through the streets[br]naked, shouting "Eureka!"

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Which comes from the ancient[br]Greek meaning "I found it."

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What did he find?

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Well, he found a way[br]to solve the king's problem.

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You see, Archimedes needed[br]to check the crown's density

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to see if it was the same[br]as the density of pure gold.

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Density is a measure of an object's mass[br]divided by its volume.

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Pure gold is very dense,[br]while silver is less dense.

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So if there was silver in the crown, it would be[br]less dense than if it were made of pure gold.

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But no matter what it was made of,[br]the crown would be the same shape,

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which means the same volume.

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So if Archimedes could measure[br]the mass of the crown first,

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and then measure its volume,

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he could find out how dense it was.

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But it is not easy to measure[br]a crown's volume - it has an irregular shape,

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that's different[br]from a simple box or ball.

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You can't measure its size and multiply[br]like you might for other shapes.

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The solution, Archimedes realized,

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was to give the crown a bath.

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by placing it in water and seeing[br]how much water was displaced,

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he could measure the volume,

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and he'd calculate[br]the density of the crown.

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If the crown was less[br]dense than pure gold,

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then the goldsmith most definitely[br]cheated the king.

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When Archimedes went back[br]to the king and did his test,

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the story says, he found that the goldsmith[br]had indeed cheated the king,

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and slipped some silver in. These days,

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using the way an object displaces[br]water to measure volume is called

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Archimedes' principle. The[br]next time you take a bath,

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you can see Archimedes'[br]principle in action,

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and maybe you'll have[br]a genius idea of your own.