What did Archimedes create to defend Syracuse?

Answer 1

Archimedes elucidated the concept of density. Both crowns weighed the same. Other methods at the time to determine the purity of the gold were destructive (ie melting point comparison). When he bathed he saw that his body displaced the water and it occurred to him that the volume of displaced water was equal to the volume of himself submerged. He weighed both crowns as well as a piece of gold of similar weight. He then submerged each crown and measured the displaced water. The crown that had displaced the same amount of water as the gold piece was made of pure gold, rather than a fake.

Answer 2

he put the crown into water and then a gold ring and compared them

Answer 3

The "claw" and "burning mirrors".