How taking a bath led to Archimedes' principle - Mark Salata

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Stories of discovery and invention often begin with a problem that needs solving. Summoned by the king to investigate a suspicious goldsmith, the early Greek mathematician Archimedes stumbles upon the principle that would make him famous.

Lesson by Amdon Consulting's Mark Salata, animation by TED-Ed.

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.