WEBVTT

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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
begin to wonder and question.

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These moments have happened
throughout history.

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and have led to some truly
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
of Syracuse in Sicily.

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He was a Greek mathematician,
physicist, engineer,

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inventor, and astronomer.

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One day, Archimedes was summoned
by the king of Sicily

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to investigate if he had
been cheated by a goldsmith.

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The king said he had given a goldsmith
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
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
to solve the problem.

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But there was a catch: he couldn't
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
level in the bathtub rose

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and overflowed as he immersed
himself into the tub.

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He suddenly realized that how much
water was displaced

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depended on how much
of his body was immersed.

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

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and ran through the streets
naked, shouting "Eureka!"

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

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What did he find?

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

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

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

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

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Pure gold is very dense,
while silver is less dense.

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

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But no matter what it was made of,
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
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
a crown's volume - it has an irregular shape,

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that's different
from a simple box or ball.

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You can't measure its size and multiply
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
how much water was displaced,

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he could measure the volume,

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and he'd calculate
the density of the crown.

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If the crown was less
dense than pure gold,

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then the goldsmith most definitely
cheated the king.

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

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the story says, he found that the goldsmith
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
water to measure volume is called

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

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you can see Archimedes'
principle in action,

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