[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:14.00,0:00:15.98,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: 0,0:00:18.02,0:00:20.98,Default,,0000,0000,0000,,Those moments in which you\Nbegin to wonder and question.
Dialogue: 0,0:00:21.00,0:00:23.24,Default,,0000,0000,0000,,These moments have happened\Nthroughout history.
Dialogue: 0,0:00:23.26,0:00:25.50,Default,,0000,0000,0000,,and have led to some truly\Namazing discoveries.
Dialogue: 0,0:00:25.53,0:00:26.98,Default,,0000,0000,0000,,Take this story, for example.
Dialogue: 0,0:00:27.00,0:00:28.98,Default,,0000,0000,0000,,There once was a fellow named Archimedes.
Dialogue: 0,0:00:29.00,0:00:31.98,Default,,0000,0000,0000,,He was born in 287 B.C. in the city\Nof Syracuse in Sicily.
Dialogue: 0,0:00:32.00,0:00:34.98,Default,,0000,0000,0000,,He was a Greek mathematician,\Nphysicist, engineer,
Dialogue: 0,0:00:35.00,0:00:36.98,Default,,0000,0000,0000,,inventor, and astronomer.
Dialogue: 0,0:00:37.00,0:00:39.98,Default,,0000,0000,0000,,One day, Archimedes was summoned\Nby the king of Sicily
Dialogue: 0,0:00:40.00,0:00:42.98,Default,,0000,0000,0000,,to investigate if he had\Nbeen 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\Nthe exact amount of gold
Dialogue: 0,0:00:46.02,0:00:47.98,Default,,0000,0000,0000,,needed to make a crown.
Dialogue: 0,0:00:48.00,0:00:51.98,Default,,0000,0000,0000,,However, when the crown was ready, the king\Nsuspected that the goldsmith cheated
Dialogue: 0,0:00:52.00,0:00:53.98,Default,,0000,0000,0000,,and slipped some silver into the crown,
Dialogue: 0,0:00:54.00,0:00:55.98,Default,,0000,0000,0000,,keeping some of the gold for himself.
Dialogue: 0,0:00:56.00,0:00:58.98,Default,,0000,0000,0000,,The king asked Archimedes\Nto solve the problem.
Dialogue: 0,0:00:59.00,0:01:03.98,Default,,0000,0000,0000,,But there was a catch: he couldn't\Ndo any damage to the crown.
Dialogue: 0,0:01:04.00,0:01:05.98,Default,,0000,0000,0000,,One day, while taking his bath,
Dialogue: 0,0:01:06.00,0:01:08.98,Default,,0000,0000,0000,,Archimedes noticed that the water\Nlevel in the bathtub rose
Dialogue: 0,0:01:09.00,0:01:11.98,Default,,0000,0000,0000,,and overflowed as he immersed\Nhimself into the tub.
Dialogue: 0,0:01:12.00,0:01:14.98,Default,,0000,0000,0000,,He suddenly realized that how much\Nwater was displaced
Dialogue: 0,0:01:15.00,0:01:17.98,Default,,0000,0000,0000,,depended on how much\Nof his body was immersed.
Dialogue: 0,0:01:18.00,0:01:21.05,Default,,0000,0000,0000,,This discovery excited him so much\Nthat he jumped out of the tub
Dialogue: 0,0:01:21.07,0:01:23.98,Default,,0000,0000,0000,,and ran through the streets\Nnaked, shouting "Eureka!"
Dialogue: 0,0:01:24.00,0:01:26.98,Default,,0000,0000,0000,,Which comes from the ancient\NGreek meaning "I found it."
Dialogue: 0,0:01:27.00,0:01:28.98,Default,,0000,0000,0000,,What did he find?
Dialogue: 0,0:01:29.00,0:01:31.29,Default,,0000,0000,0000,,Well, he found a way\Nto solve the king's problem.
Dialogue: 0,0:01:31.31,0:01:33.98,Default,,0000,0000,0000,,You see, Archimedes needed\Nto check the crown's density
Dialogue: 0,0:01:34.00,0:01:36.98,Default,,0000,0000,0000,,to see if it was the same\Nas 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\Ndivided by its volume.
Dialogue: 0,0:01:40.02,0:01:42.98,Default,,0000,0000,0000,,Pure gold is very dense,\Nwhile silver is less dense.
Dialogue: 0,0:01:43.00,0:01:47.98,Default,,0000,0000,0000,,So if there was silver in the crown, it would be\Nless dense than if it were made of pure gold.
Dialogue: 0,0:01:48.00,0:01:51.29,Default,,0000,0000,0000,,But no matter what it was made of,\Nthe crown would be the same shape,
Dialogue: 0,0:01:51.31,0:01:52.98,Default,,0000,0000,0000,,which means the same volume.
Dialogue: 0,0:01:53.00,0:01:54.98,Default,,0000,0000,0000,,So if Archimedes could measure\Nthe mass of the crown first,
Dialogue: 0,0:01:55.00,0:01:56.98,Default,,0000,0000,0000,,and then measure its volume,
Dialogue: 0,0:01:57.00,0:01:58.98,Default,,0000,0000,0000,,he could find out how dense it was.
Dialogue: 0,0:01:59.00,0:02:01.98,Default,,0000,0000,0000,,But it is not easy to measure\Na crown's volume - it has an irregular shape,
Dialogue: 0,0:02:02.00,0:02:04.05,Default,,0000,0000,0000,,that's different\Nfrom a simple box or ball.
Dialogue: 0,0:02:04.07,0:02:07.98,Default,,0000,0000,0000,,You can't measure its size and multiply\Nlike you might for other shapes.
Dialogue: 0,0:02:08.00,0:02:10.98,Default,,0000,0000,0000,,The solution, Archimedes realized,
Dialogue: 0,0:02:11.00,0:02:12.98,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\Nhow much water was displaced,
Dialogue: 0,0:02:16.02,0:02:17.98,Default,,0000,0000,0000,,he could measure the volume,
Dialogue: 0,0:02:18.00,0:02:20.98,Default,,0000,0000,0000,,and he'd calculate\Nthe density of the crown.
Dialogue: 0,0:02:21.00,0:02:23.05,Default,,0000,0000,0000,,If the crown was less\Ndense than pure gold,
Dialogue: 0,0:02:23.07,0:02:25.98,Default,,0000,0000,0000,,then the goldsmith most definitely\Ncheated the king.
Dialogue: 0,0:02:26.00,0:02:28.98,Default,,0000,0000,0000,,When Archimedes went back\Nto the king and did his test,
Dialogue: 0,0:02:29.00,0:02:32.98,Default,,0000,0000,0000,,the story says, he found that the goldsmith\Nhad indeed cheated the king,
Dialogue: 0,0:02:33.00,0:02:35.98,Default,,0000,0000,0000,,and slipped some silver in. These days,
Dialogue: 0,0:02:36.00,0:02:39.19,Default,,0000,0000,0000,,using the way an object displaces\Nwater to measure volume is called
Dialogue: 0,0:02:39.22,0:02:41.98,Default,,0000,0000,0000,,Archimedes' principle. The\Nnext time you take a bath,
Dialogue: 0,0:02:42.00,0:02:44.98,Default,,0000,0000,0000,,you can see Archimedes'\Nprinciple in action,
Dialogue: 0,0:02:45.00,0:02:49.00,Default,,0000,0000,0000,,and maybe you'll have\Na genius idea of your own.