variety of bodies. In mathematics, Archimedes also

developed methods for solving cubic equations,

approximating square roots, summing

SERIES

, and, in

The Sand Reckoning, developed a notation for repre-

senting extremely large numbers.

Except for taking time to study at E

UCLID

’s school in

Alexandria, Archimedes spent his entire life at the place

of his birth. He was a trusted friend of the monarch of

the region, Hiero, and his son Gelon, and soon devel-

oped a reputation as a brilliant scientist who could solve

the king’s most troublesome problems. One famous

story asserts that the king once ordered a goldsmith to

make him a crown, and supplied the smith the exact

amount of metal to make it. Upon receiving the newly

forged crown, Hiero suspected the smith of ill doing,

substituting some cheaper silver for the gold, even

though the crown did have the correct weight. He could

not prove his suspicions were correct, however, and so

brought the problem to Archimedes. It is said that while

bathing and observing the water displaced by his body

Archimedes realized, and proved, that the weight of an

object suspended in liquid decreases in proportion to the

weight of the liquid it displaces. This principle, today

known as Archimedes’ principle, provided Archimedes

the means to indeed prove that the crown was not of

solid gold. (It is also said that Archimedes was so excited

upon making this discovery that he ran naked through

the streets shouting, “Eureka! Eureka!”)

Archimedes is also purported to have said, “Give me

a place to stand and I shall move the Earth.” Astonished

Archimedes of Syracuse 19

A 1547 woodcut depicting Archimedes’ realization that a tub of water can be used to compute the volumes and densities of solid figures

(Photo courtesy of ARPL/Topham/The Image Works)