Around 200 BC, Sicily was ruled by a king known as Hiero. The king gave a goldsmith a certain amount of pure gold and ordered the smith was to make him a crown from it. After receiving the finished crown, the king suspected that the goldsmith had deceived him by mixing silver with the gold taking some of the gold for himself. The king's friend Archimedes (287-212 BC) was commissioned to find out if the king's doubts were true.

According to the story, one day Archimedes went to take a bath. He stepped into a bath tub that was filled to the brim with water. As he watched the excess water flow from the tub to the floor, Archimedes realized that his body volume was displacing the same volume of water from the tub. He had found out how to solve the problem of the king's crown. By submerging them in water, Archimedes would be able to compare the volumes of the crown and a pure piece of gold without melting and ruining the crown. He was so inspired that he leapt up from his bath and began to run along the streets of Syracuse, shouting "Eureka, eureka!", which means "I have invented it!".

Archimedes solved the problem of the king's crown by dropping it into a container filled with water and measuring the volume of water that flowed over the edges of the container. He then dropped exactly the same amount of gold into a similar container and measured the volume of water flowing over its edges. If the crown was actually made of pure gold, the amount of water flowing over should have been equal in both cases. However, this was not the case. The goldsmith had actually stolen some of the gold for himself. Perhaps, however, he was only being professional, as a crown made of pure gold would not have withstood the knocks of regular use.