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Archimedes greatest contributions were in geometry. His methods anticipated the integral calculus 2,000 years before Newton and Leibniz.Archimedes was a native of Syracuse, Sicily. Stories from Plutarch, Livy, and others describe machines invented by Archimedes for the defence of Syracuse. These include the catapult, the compound pulley and a burning-mirror.
Among Archimedes most famous works is Measurement of the Circle , in which he put the exact value of between the values 3/ and 3/. This he obtained by circumscribing and inscribing a circle with regular polygons having 96 sides.
Archimedes proved, among many other geometrical results, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder. This he considered his most significant accomplishments, requesting that a representation of a cylinder circumscribing a sphere be inscribed on his tomb.
His fascination with geometry is beautifully described by Plutarch.
Oftimes Archimedes' servants got him against his will to the baths, to wash and anoint him; and yet being there, he would ever be drawing out of the geometrical figures, even in the very embers of the chimney. And while they were anointing of him with oils and sweet savours, with his fingures he drew lines upon his naked body; so far was he taken from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry.Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and solids. His most famous theorem gives the weight of a body immersed in a liquid, called Archimedes' principal.
Archimedes' mechanical skill together with his theoretical knowledge enabled him to construct many ingenious machines. Archimedes spent some time in Egypt, where he invented a device now known as Archimedes' screw. This is a pump, still used in many parts of the world.
He was killed during the capture of Syracuse by the Romans in the Second Punic War. Plutarch recounts this story of his killing:
As fate would have it, Archimedes was intent on working out some problem by a diagram, and having fixed both his mind and eyes upon the subject of his speculation, he did not notice the entry of the Romans nor that the city was taken. In this transport of study a soldier unexpectedly came up to him and commanded that he accompany him. When he declined to do this before he had finished his problem, the enraged soldier drew his sword and ran him through.
References (80 books/articles)
A page from a work by Archimedes:
A page from Cremona's translation of On the Sphere and Cylinder
References elsewhere in this archive:
Tell me about some semi-regular (or Archimedean) solids
Tell me about Archimedes' cattle problem and about its solution
Tell me about the Cissoid of Diocles
Tell me about Archimedes' spiral
Tell me about the hyperbolic spiral
Tell me about the method of exhaustion and its use in calculating
There is a Crater Archimedes on the moon. There is also a Rimae Archimedes. There are also Montes Archimedes. You can see a list of lunar features named after mathematicians.
Other Web sites:
Clarke University, USA
Library of Congress, USA
University of Virginia, USA
New Jersey, USA
Drexel University, USA
There is some information about Arcimedes' calculation of square roots at Seattle, USA
You can read Plutarch's account of Archimedes' war machines and of his death at MIT, USA
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