 |
|
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,
excelling especially at computing areas and volumes using the method of
exhaustion.  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 was 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.
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,
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.
Additional biographies: MacTutor
(St. Andrews), Firenze,
Bonn,
Greek
and Roman Science and Technology
References
Bell, E. T. "Modern Minds in Ancient Bodies: Zeno, Eudoxus,
Archimedes." Ch. 2 in Men
of Mathematics: The Lives and Achievements of the Great
Mathematicians from Zeno to Poincaré. New York: Simon and
Schuster, pp. 19-34, 1986.
Dijksterhuis, E. J. Archimedes.
Princeton, NJ: Princeton University Press, 1987.
Dunham, W. "Archimedes' Determination of Circular Area."
Ch. 4 in Journey
Through Genius: The Great Theorems of Mathematics. New York:
Wiley, pp. 84-112, 1990.
Heath, T. L. The Works of Archimedes. New York:
Dover, 1953.
Kleiner, K. "Lasers Reveal Ancient Words of Wisdom." New
Scientist 167, 6, 22 Jul 2000.
Plutarch. Life of Marcellus.
Rorres, C. "Archimedes." http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html.
Stein, S. Archimedes:
What Did He Do Besides Cry Eureka? Washington, DC: Amer.
Math. Soc., 1999.
Author: Eric W. Weisstein
|
