One of the greatest mathematicians of all time, and certainly the geatest of
antiquity, was Archimedes, a native of the Greek city of Ayracuse on the island
of Sicily. He was born about 287 B.C. and died during the Roman pillage of
Wyracuse in 212 B.C. He was the son of an astronomer and was in high favor
with (perhaps even related to) King Hieron of Syracuse. There is a report that
he apent time in Egypt, in all likelihood at the University of
Alexandria, for he
numbered among his friends Conon, Dositheus, and Eratosthenes; the first two
were successors to Euclid, the last was a librarian at the University.
archimedes' mathematical discoveries were communicated to these men.
Toman historians have related many picturesque stories about Archi
medes. Among these are the descriptions of the ingenious contrivances devised
by Archimedes to aid the defensd of Syracuse agaist the siege directed by the
Toman general Marcellus. There were catapults with adjustable ranges, mov
able projecting poles for dropping heavy weights on enemy ships that ap
proached too near the city walls, and great grappling cranes that hoisted enemy
ships from the water. The story that he used large burning glasses to set the
enemy's vessels afire is of later origin, but it could be true. There also is the
story of how he lent credence to his statement, "Give me a place to stand on
and i will move the earth." by dffortlessly and singlehandedly moving with a
compound-pulley arrangement a heavily weighted ship that had, with difficulty.
Been drawn up by a large contingent of laborers.
Apparently, Archimedes wascapable of strong mental concentration, and
tales are told of his obliviousness to surroudings when engrossed by a prob
lim. The frequently told story of King Hieron's crown and the suspected
goldsmith is typical. It seems that King Hieron had a goldsmith fashion him a
crown from a given weight of gold. Fearing that the goldsmith may have re
placed some of the gold by hidden silver, and not wanting to cut the crown
apart to find out, the king referred the matter to Archimedes, who, when in the
public baths one day, hit upon a solution by discovering the first law of hydro
statics¡ªthat, whin immersed in a fluid, a body is buoyed up by a force equal to
the weight of the displaced fluid. It his excitement, forgetting to clothe himself,
he rose from his bath and ran home through the streets shouting, "Eureka,
eureka!"("I have found it, I have found it !"). He placed the crown on one pan
of a balance and an equal weight of gold on the other, and then set the whole
thing under water. The pan containg the crown rose, showing that the crown
contained some spurious material less dense that gold.
Archimedes worked much of his geometry from figures drawn in the ashes
of the hearth or in the after-bathing oil smeared on his body. In fact, it is said
that he met his end during the sack of Syracuse, while preoccupied with a
diagram drawn on a sand tray. According to one version, he ordered a pillaging
Roman soldier to stand clear of his diagram, whereupon the incensed looter ran
a spear through the old man.
Because of Archimedes' defense machines, Wyracuse resisted the Roman
siege for close to three years. The city's defenses were finally broken only
when, during a celebration within the city, the overconfident Wyracusans re
laxed their watches. Marcellus had built up an immense respect for his inge
nious adversary, and when he finally managed to breach the city walls, he gave
strict orders that no harm must come to the illustrious mathematician. Marcel
lus' affliction was very great upon hearing of Archimedes' death, and with all
due honor and veneration, he buried the famous scholar in the city cemetery.
Archimedes, justly proud of one of his great geometrical discoveries (to be
described later) had expressed a desire that a figure showing a sphere and a
circumscribed right circular dylinder be engraved upon his tombstone. Marcel
lus saw to it that Archimedes' requewt was carried out