FREE ESSAY ON ARCHIMEDES OF SYRACUSE

ARCHIMEDES OF SYRACUSE

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 f 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. During the Roman siege of Syracuse, he is said to
have single-handedly defended the city by constructing lenses to focus the Sun's light on
Roman ships and huge cranes to turn them upside down. When the Romans finally broke the
siege, Archimedes was killed by a Roman soldier after snapping at him ``Don't disturb my
circles,'' a reference to a geometric figure he had outlined on the sand.