In an excerpt from his new book, John Monahan recounts the story of Archimedes, the scientist who coined the term "Eureka" when tasked with figuring out whether the king's crown was made of pure gold:

[Archimedes] was visiting a public bath, and as he stepped into the tub of water, it began to overflow. The more he immersed himself in the water, the more it overflowed. He realized that the amount of water being spilled was proportional to the volume of the body being placed into the water. He further made the connection that if he placed the crown into a given amount of water, and it displaced more water than the same weight of pure gold, then the crown and the pure gold must have a different volume. In other words, if they had a different volume, then the crown could not be pure gold.

He was so excited by his discovery that he leaped from the tub and ran home through the streets, still wet and naked, yelling, “I have it! I have it!” The word for this in ancient Greek is Eureka! The king was delighted by the brilliance of Archimedes’ insight. The goldsmith was not. Archimedes’ test worked. The crown was not pure gold, and the hapless smith was executed.

We want to hear what you think about this article. Submit a letter to the editor or write to letters@theatlantic.com.