Who discovered how to authenticate a gold crown without damaging it?
Should this be in the history section?
I think you refer to the story of Hiero, tyrant of Syracuse, who, in the 3rd century BC, suspected that one of his goldsmiths had used a baser metal than gold to construct a prized crown. Hiero called upon Archimedes, one of the most accomplished scientists and physicists of his day (possibly of any day) to investigate the matter. Archimedes used the concept of density (and this concept Archimedes had to develop), mass per unit volume, to find that the goldsmith had in fact been a bit light fingered with the gold entrusted to him.
Anyway, there should be accounts of this on the web. By tradition, Archimedes used water displacement to measure the volume of a solid denser than water to measure the volume of the solid. He was supposed to be taking a bath, when he noticed the displacement of water:
Poor old Archimedes was later killed in the Roman siege of Syracuse a few years later.