Some of the best opportunities to learn
are the moments in which we are perplexed.
Those moments in which you begin to wonder and question.
These moments have happened throughout history.
and have led to some truly amazing discoveries.
Take this story, for example.
There once was a fellow named Archimedes.
He was born in 287 B.C. in the city of Syracuse in Sicily.
He was a Greek mathematician, physicist, engineer,
inventor, and astronomer.
One day, Archimedes was summoned by the king of Sicily
to investigate if he had been cheated by a goldsmith.
The king said he had given a goldsmith the exact amount of gold
needed to make a crown.
However, when the crown was ready, the king suspected that the goldsmith cheated
and slipped some silver into the crown,
keeping some of the gold for himself.
The king asked Archimedes to solve the problem.
But there was a catch: he couldn't do any damage to the crown.
One day, while taking his bath,
Archimedes noticed that the water level in the bathtub rose
and overflowed as he immersed himself into the tub.
He suddenly realized that how much water was displaced
depended on how much of his body was immersed.
This discovery excited him so much that he jumped out of the tub
and ran through the streets naked, shouting "Eureka!"
Which comes from the ancient Greek meaning "I found it."
What did he find?
Well, he found a way to solve the king's problem.
You see, Archimedes needed to check the crown's density
to see if it was the same as the density of pure gold.
Density is a measure of an object's mass divided by its volume.
Pure gold is very dense, while silver is less dense.
So if there was silver in the crown, it would be less 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 measure the mass of the crown first,
and then measure its volume,
he could find out how dense it was.
But it is not easy to measure a crown's volume - it has an irregular shape,
that's different from a simple box or ball.
You can't measure its size and multiply like you might for other shapes.
The solution, Archimedes realized,
was to give the crown a bath.
by placing it in water and seeing how much water was displaced,
he could measure the volume,
and he'd calculate the density of the crown.
If the crown was less dense than pure gold,
then the goldsmith most definitely cheated the king.
When Archimedes went back to the king and did his test,
the story says, he found that the goldsmith had indeed cheated the king,
and slipped some silver in. These days,
using the way an object displaces water to measure volume is called
Archimedes' principle. The next time you take a bath,
you can see Archimedes' principle in action,
and maybe you'll have a genius idea of your own.