The king of Greece commissioned a blacksmith to make him a gold crown but suspected he was tricked and given a crown containing silver instead of pure gold. He asked Archimedes for help solving this problem. Archimedes realized in the bath that he could determine the crown's composition by measuring how much water it displaces compared to an equal weight of gold. He excitedly informed the king he had found a solution and tested the crown's density in water, discovering it contained silver according to Archimedes' principle of displacement.