Archimedes (287-212 BC) was a Greek polymath who was known as one of the leading scientists of the Classical period. Born in Syracuse, he became well-known at the court of King Hiero II of Syracuse due to his inventions, including his innovations in calculus and analysis, his contributions to mathematics (such as how to find the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, and the area of a spiral, etc.), his approximation of pi, his devising of a system of exponents to portray very large numbers, invented the lever, conceptualized the idea of a center of gravity and the law of buoyancy, and designed a screw pump, compound pulleys, and war machines such as a claw to lift ships out of water and a parabolic reflector used as a heat ray. Archimedes was also well known as a charmer, having an affair with the dancer Artemis while engaged to marry Hiero's daughter Clio. In 213-212 BC, he utilized his inventions during the defense of Syracuse against a Roman siege amid the Second Punic War, but, against the orders of the Roman general Marcus Claudius Marcellus, Roman soldiers slew Archimedes on confronting him.