# Archimedes

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Archimedes

Archimedes of Syracuse (ca. 287-ca. 212 BC)

Greek mathematician who flourished in Sicily. He is generally considered to be the greatest mathematician of ancient times. Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch.

Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid (Greek geometer who wrote the Elements, the world's most definitive text on geometry.), excelling especially at computing areas and volumes using the METHOD OF EXHAUSTION(a integral-like limiting process to compute the area and volume of 2-D lamina and 3-D solids.).

2-D Lamina¡¦s:

3-D Solids

He was especially proud of his discovery for finding the volume of a sphere, showing that it is two thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder as engraved on his tombstone.

In fact, it is often said that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation. By inscribing and circumscribing polygons on a circle, for instance, he was able to constrain the value of (pi ) between 3 10/71 and 3+1/7.

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Archimedes was also an outstanding engineer, formulating Archimedes' principle of buayancy and the law of the lever. Legend has it that Archimedes discovered his principle of buoyancy, which states that the buoyancy force is equal to the weight of the liquid displaced, while taking a bath, upon which he is supposed to have run naked through the streets of Syracuse shouting ``Eureka!'' (I have found it). Archimedes is also purported to have invented the Archimedean screw.

Some of Archimedes's geometric proofs were actually motivated by mechanical arguments which led him to the correct answer.