WEBVTT 00:00:14.000 --> 00:00:16.000 Some of the best opportunities to learn 00:00:16.000 --> 00:00:18.000 are the moments in which we are perplexed. 00:00:18.000 --> 00:00:21.000 Those moments in which you begin to wonder and question. 00:00:21.000 --> 00:00:23.000 These moments have happened throughout history. 00:00:23.000 --> 00:00:25.000 and have led to some truly amazing discoveries. 00:00:25.000 --> 00:00:27.000 Take this story, for example. 00:00:27.000 --> 00:00:29.000 There once was a fellow named Archimedes. 00:00:29.000 --> 00:00:32.000 He was born in 287 B.C. in the city of Syracuse in Sicily. 00:00:32.000 --> 00:00:35.000 He was a Greek mathematician, physicist, engineer, 00:00:35.000 --> 00:00:37.000 inventor, and astronomer. 00:00:37.000 --> 00:00:40.000 One day, Archimedes was summoned by the king of Sicily 00:00:40.000 --> 00:00:43.000 to investigate if he had been cheated by a goldsmith. 00:00:43.000 --> 00:00:46.000 The king said he had given a goldsmith the exact amount of gold 00:00:46.000 --> 00:00:48.000 needed to make a crown. 00:00:48.000 --> 00:00:52.000 However, when the crown was ready, the king suspected that the goldsmith cheated 00:00:52.000 --> 00:00:54.000 and slipped some silver into the crown, 00:00:54.000 --> 00:00:56.000 keeping some of the gold for himself. 00:00:56.000 --> 00:00:59.000 The king asked Archimedes to solve the problem. 00:00:59.000 --> 00:01:04.000 But there was a catch: he couldn't do any damage to the crown. 00:01:04.000 --> 00:01:06.000 One day, while taking his bath, 00:01:06.000 --> 00:01:09.000 Archimedes noticed that the water level in the bathtub rose 00:01:09.000 --> 00:01:12.000 and overflowed as he immersed himself into the tub. 00:01:12.000 --> 00:01:15.000 He suddenly realized that how much water was displaced 00:01:15.000 --> 00:01:18.000 depended on how much of his body was immersed. 00:01:18.000 --> 00:01:21.000 This discovery excited him so much that he jumped out of the tub 00:01:21.000 --> 00:01:24.000 and ran through the streets naked, shouting "Eureka!" 00:01:24.000 --> 00:01:27.000 Which comes from the ancient Greek meaning "I found it." 00:01:27.000 --> 00:01:29.000 What did he find? 00:01:29.000 --> 00:01:31.000 Well, he found a way to solve the king's problem. 00:01:31.000 --> 00:01:34.000 You see, Archimedes needed to check the crown's density 00:01:34.000 --> 00:01:37.000 to see if it was the same as the density of pure gold. 00:01:37.000 --> 00:01:40.000 Density is a measure of an object's mass divided by its volume. 00:01:40.000 --> 00:01:43.000 Pure gold is very dense, while silver is less dense. 00:01:43.000 --> 00:01:48.000 So if there was silver in the crown, it would be less dense than if it were made of pure gold. 00:01:48.000 --> 00:01:51.000 But no matter what it was made of, the crown would be the same shape, 00:01:51.000 --> 00:01:53.000 which means the same volume. 00:01:53.000 --> 00:01:55.000 So if Archimedes could measure the mass of the crown first, 00:01:55.000 --> 00:01:57.000 and then measure its volume, 00:01:57.000 --> 00:01:59.000 he could find out how dense it was. 00:01:59.000 --> 00:02:02.000 But it is not easy to measure a crown's volume - it has an irregular shape, 00:02:02.000 --> 00:02:04.000 that's different from a simple box or ball. 00:02:04.000 --> 00:02:08.000 You can't measure its size and multiply like you might for other shapes. 00:02:08.000 --> 00:02:11.000 The solution, Archimedes realized, 00:02:11.000 --> 00:02:13.000 was to give the crown a bath. 00:02:13.000 --> 00:02:16.000 by placing it in water and seeing how much water was displaced, 00:02:16.000 --> 00:02:18.000 he could measure the volume, 00:02:18.000 --> 00:02:21.000 and he'd calculate the density of the crown. 00:02:21.000 --> 00:02:23.000 If the crown was less dense than pure gold, 00:02:23.000 --> 00:02:26.000 then the goldsmith most definitely cheated the king. 00:02:26.000 --> 00:02:29.000 When Archimedes went back to the king and did his test, 00:02:29.000 --> 00:02:33.000 the story says, he found that the goldsmith had indeed cheated the king, 00:02:33.000 --> 00:02:36.000 and slipped some silver in. These days, 00:02:36.000 --> 00:02:39.000 using the way an object displaces water to measure volume is called 00:02:39.000 --> 00:02:42.000 Archimedes' principle. The next time you take a bath, 00:02:42.000 --> 00:02:45.000 you can see Archimedes' principle in action, 00:02:45.000 --> 00:02:49.000 and maybe you'll have a genius idea of your own.