“Eureka! Eureka!” shouts could be heard from around town as a brazen Archimedes streaked through the streets of Syracuse bare. “Eureka!” he shouted all the way home. He felt nothing but pure excitement at his latest discovery. He had just come from the bath where he stuck his foot in and saw the water rise. Eureka!
Archimedes had been contracted by the tyrant King Heiro II to find a way to check if his crown was pure gold. The King had suspected that a bit of silver had been used in making the crown. Archimedes’ first solution, if the King was so sure, was to crush the crown into a small cube where the volume could easily be measured and compared with the mass. Density (the ratio of mass to volume) was a well known concept, as was the fact that gold is more dense than silver. The King would not allow this. Archimedes, in a huff, took to the bath where the famed moment occurred. Eureka! He had discovered that one can measure the volume of the object simply by measuring the volume of water that had been displaced.
This meant that he could take the crown and submerge it, then find the volume of the crown my measuring the displacement of water.
While the crown does not appear in the work of Archimedes, it is the most well known legend of the man.