ArchimedesArchimedes of Syracuse (ca. 287-ca. 212 BC)Greek mathematician who flourished in Sicily. He is generally considered the greatest mathematician of ancient times. Most of the facts about his life come from a biography of the Roman soldier Marcellus written by the Roman biographer Plutarch. Archimedes performed numerous geometric tests using the rigid geometric formalism outlined by Euclid (Greek geometer who wrote the Elements, the most definitive text in the world on the subject) geometry.), excelling above all in the calculation of areas and volumes using the METHOD OF EXHAUSTION (a integral-like limiting process for calculating the area and volume of 2-D plate and 3-D Solids.).2-D Plate¡¦s: 3-D SolidsHe 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 a cylinder was engraved on his tombstone. Indeed, it is often said that Archimedes would have invented calculus if only the Greeks had possessed more tractable mathematical notation. By inscribing and circumscribing polygons on a circle, for example, he was able to constrain the value of (pi) between 3 10/71 and 3+1/7. Archimedes was also an outstanding engineer, formulating Archimedes' principle of buoyancy and the law of the lever. Legend has it that Archimedes discovered his principle of buoyancy, according to which the buoyancy force is equal to the weight of the displaced liquid, while taking a bath, during which he supposedly ran naked through the streets of Syracuse shouting 'Eureka!' ' (I found it.) It is also assumed that Archimedes invented the Archimedes screw. Some of Archimedes' geometric proofs were actually motivated by mechanical arguments which led him to the correct answer.