[Answer] 1. Eureka! Which ancient Greek mathematician discovered the principles of density and buoyancy after King Hiero II challenged him to authenticate his crown?

Step 1 : Introduction to the question "1. Eureka! Which ancient Greek mathematician discovered the principles of density and buoyancy after King Hiero II challenged him to authenticate his crown?"

...1. Plato 2. Archimedes 3. Sophocles 4. Aristotle Hiero II, king of Syracuse, commissioned a gold crown for a temple, as an offering to the gods. When he became suspicious of the goldsmith's actions, he challenged Archimedes to find a way to verify the purity of the crown without damaging it: after all, you wouldn't want to damage an authentic crown. Archimedes had a flash of inspiration while taking a bath. He noticed water spilling over the top when he got in, and this suggested the principle of density or buoyancy to him. He became so excited that he ran through the streets naked, shouting "Eureka!," and this is what he is most notorious for today. The crown was found to be debased, and the goldsmith dealt with accordingly.

Step 2 : Answer to the question "1. Eureka! Which ancient Greek mathematician discovered the principles of density and buoyancy after King Hiero II challenged him to authenticate his crown?"

Archimedes:

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