[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:14.00,0:00:16.00,Default,,0000,0000,0000,,Some of the best opportunities to learn
Dialogue: 0,0:00:16.00,0:00:18.00,Default,,0000,0000,0000,,are the moments in which we are perplexed.
Dialogue: 0,0:00:18.00,0:00:21.00,Default,,0000,0000,0000,,Those moments in which you begin to wonder and question.
Dialogue: 0,0:00:21.00,0:00:23.00,Default,,0000,0000,0000,,These moments have happened throughout history.
Dialogue: 0,0:00:23.00,0:00:25.00,Default,,0000,0000,0000,,and have led to some truly amazing discoveries.
Dialogue: 0,0:00:25.00,0:00:27.00,Default,,0000,0000,0000,,Take this story, for example.
Dialogue: 0,0:00:27.00,0:00:29.00,Default,,0000,0000,0000,,There once was a fellow named Archimedes.
Dialogue: 0,0:00:29.00,0:00:32.00,Default,,0000,0000,0000,,He was born in 287 B.C. in the city of Syracuse in Sicily.
Dialogue: 0,0:00:32.00,0:00:35.00,Default,,0000,0000,0000,,He was a Greek mathematician, physicist, engineer,
Dialogue: 0,0:00:35.00,0:00:37.00,Default,,0000,0000,0000,,inventor, and astronomer.
Dialogue: 0,0:00:37.00,0:00:40.00,Default,,0000,0000,0000,,One day, Archimedes was summoned by the king of Sicily
Dialogue: 0,0:00:40.00,0:00:43.00,Default,,0000,0000,0000,,to investigate if he had been cheated by a goldsmith.
Dialogue: 0,0:00:43.00,0:00:46.00,Default,,0000,0000,0000,,The king said he had given a goldsmith the exact amount of gold
Dialogue: 0,0:00:46.00,0:00:48.00,Default,,0000,0000,0000,,needed to make a crown.
Dialogue: 0,0:00:48.00,0:00:52.00,Default,,0000,0000,0000,,However, when the crown was ready, the king suspected that the goldsmith cheated
Dialogue: 0,0:00:52.00,0:00:54.00,Default,,0000,0000,0000,,and slipped some silver into the crown,
Dialogue: 0,0:00:54.00,0:00:56.00,Default,,0000,0000,0000,,keeping some of the gold for himself.
Dialogue: 0,0:00:56.00,0:00:59.00,Default,,0000,0000,0000,,The king asked Archimedes to solve the problem.
Dialogue: 0,0:00:59.00,0:01:04.00,Default,,0000,0000,0000,,But there was a catch: he couldn't do any damage to the crown.
Dialogue: 0,0:01:04.00,0:01:06.00,Default,,0000,0000,0000,,One day, while taking his bath,
Dialogue: 0,0:01:06.00,0:01:09.00,Default,,0000,0000,0000,,Archimedes noticed that the water level in the bathtub rose
Dialogue: 0,0:01:09.00,0:01:12.00,Default,,0000,0000,0000,,and overflowed as he immersed himself into the tub.
Dialogue: 0,0:01:12.00,0:01:15.00,Default,,0000,0000,0000,,He suddenly realized that how much water was displaced
Dialogue: 0,0:01:15.00,0:01:18.00,Default,,0000,0000,0000,,depended on how much of his body was immersed.
Dialogue: 0,0:01:18.00,0:01:21.00,Default,,0000,0000,0000,,This discovery excited him so much that he jumped out of the tub
Dialogue: 0,0:01:21.00,0:01:24.00,Default,,0000,0000,0000,,and ran through the streets naked, shouting "Eureka!"
Dialogue: 0,0:01:24.00,0:01:27.00,Default,,0000,0000,0000,,Which comes from the ancient Greek meaning "I found it."
Dialogue: 0,0:01:27.00,0:01:29.00,Default,,0000,0000,0000,,What did he find?
Dialogue: 0,0:01:29.00,0:01:31.00,Default,,0000,0000,0000,,Well, he found a way to solve the king's problem.
Dialogue: 0,0:01:31.00,0:01:34.00,Default,,0000,0000,0000,,You see, Archimedes needed to check the crown's density
Dialogue: 0,0:01:34.00,0:01:37.00,Default,,0000,0000,0000,,to see if it was the same as the density of pure gold.
Dialogue: 0,0:01:37.00,0:01:40.00,Default,,0000,0000,0000,,Density is a measure of an object's mass divided by its volume.
Dialogue: 0,0:01:40.00,0:01:43.00,Default,,0000,0000,0000,,Pure gold is very dense, while silver is less dense.
Dialogue: 0,0:01:43.00,0:01:48.00,Default,,0000,0000,0000,,So if there was silver in the crown, it would be less dense than if it were made of pure gold.
Dialogue: 0,0:01:48.00,0:01:51.00,Default,,0000,0000,0000,,But no matter what it was made of, the crown would be the same shape,
Dialogue: 0,0:01:51.00,0:01:53.00,Default,,0000,0000,0000,,which means the same volume.
Dialogue: 0,0:01:53.00,0:01:55.00,Default,,0000,0000,0000,,So if Archimedes could measure the mass of the crown first,
Dialogue: 0,0:01:55.00,0:01:57.00,Default,,0000,0000,0000,,and then measure its volume,
Dialogue: 0,0:01:57.00,0:01:59.00,Default,,0000,0000,0000,,he could find out how dense it was.
Dialogue: 0,0:01:59.00,0:02:02.00,Default,,0000,0000,0000,,But it is not easy to measure a crown's volume - it has an irregular shape,
Dialogue: 0,0:02:02.00,0:02:04.00,Default,,0000,0000,0000,,that's different from a simple box or ball.
Dialogue: 0,0:02:04.00,0:02:08.00,Default,,0000,0000,0000,,You can't measure its size and multiply like you might for other shapes.
Dialogue: 0,0:02:08.00,0:02:11.00,Default,,0000,0000,0000,,The solution, Archimedes realized,
Dialogue: 0,0:02:11.00,0:02:13.00,Default,,0000,0000,0000,,was to give the crown a bath.
Dialogue: 0,0:02:13.00,0:02:16.00,Default,,0000,0000,0000,,by placing it in water and seeing how much water was displaced,
Dialogue: 0,0:02:16.00,0:02:18.00,Default,,0000,0000,0000,,he could measure the volume,
Dialogue: 0,0:02:18.00,0:02:21.00,Default,,0000,0000,0000,,and he'd calculate the density of the crown.
Dialogue: 0,0:02:21.00,0:02:23.00,Default,,0000,0000,0000,,If the crown was less dense than pure gold,
Dialogue: 0,0:02:23.00,0:02:26.00,Default,,0000,0000,0000,,then the goldsmith most definitely cheated the king.
Dialogue: 0,0:02:26.00,0:02:29.00,Default,,0000,0000,0000,,When Archimedes went back to the king and did his test,
Dialogue: 0,0:02:29.00,0:02:33.00,Default,,0000,0000,0000,,the story says, he found that the goldsmith had indeed cheated the king,
Dialogue: 0,0:02:33.00,0:02:36.00,Default,,0000,0000,0000,,and slipped some silver in. These days,
Dialogue: 0,0:02:36.00,0:02:39.00,Default,,0000,0000,0000,,using the way an object displaces water to measure volume is called
Dialogue: 0,0:02:39.00,0:02:42.00,Default,,0000,0000,0000,,Archimedes' principle. The next time you take a bath,
Dialogue: 0,0:02:42.00,0:02:45.00,Default,,0000,0000,0000,,you can see Archimedes' principle in action,
Dialogue: 0,0:02:45.00,0:02:49.00,Default,,0000,0000,0000,,and maybe you'll have a genius idea of your own.