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ARCHIMEDES OF CYRACUS

 

ARCHIMEDES OF CYRACUS

Archimedes (ca. 287–212 BCE) was a relative of the ruler of Syracuse, Hieron II, and his father was the astronomer Phidias. Belonging to one of Syracuse’s most aristocratic families, Archimedes didn’t have to work, and mathematics became his passion. In fact, he is believed to have cared so little about daily life that he left meals uneaten when a mathematical problem occupied his mind.

Archimedes is famous for a great discovery he made while taking a bath. The episode with the bath actually begins with a request by Hieron to his bright relative to help him determine whether a goldsmith had stolen some of his gold. The king had apparently asked the goldsmith to make him a new crown, providing him with the needed gold. When the king got his new crown from the goldsmith, he became suspicious that the goldsmith had replaced some of the gold inside the crown with silver or another cheaper metal and then pocketed the missing gold. The king needed Archimedes to find a way to compare the density of the crown with the density of gold without damaging the crown. 

Archimedes pondered this dilemma while taking a bath, absently noting that the tub water rose when he got in. Suddenly it hit him: the water displaced was equal in volume to that of his body. Famously, he jumped out of the bath and ran naked through the streets of Syracuse, shouting, “Eureka, eureka!” (I found it, I found it!)

ARCHIMEDES OF CYRACUS

Archimedes now had a method for measuring the volume of an irregularly shaped object, such as a crown or a human body, by immersing it in water and measuring the volume of the water it replaces. Then, by weighing the object—the crown, in this case—one could find its density (weight divided by volume). And by comparing this density with that of gold, one could determine whether the goldsmith had cheated the king and stolen his gold! We don’t know whether the goldsmith was found guilty or not, however.

Beyond this discovery, Archimedes helped his king and the people of Syracuse fight against the invading Romans by inventing many machines useful in warfare, including various kinds of catapults and (supposedly) a set of mirrors that focused the sun’s rays on attacking ships, causing them to burn, although there’s no strong proof that this last invention was viable. Many of the weapons he invented enabled the Syracusans to defend themselves—at least for a while—against Roman attack.

 

ARCHIMEDEAN PROBLRM

Archimedes also applied Eudoxus’s amazingly powerful analysis to the study of the areas and volumes of solids. As such, his work also anticipated the development of calculus. He is also known for discovering the Archimedean spiral, which is the locus of all points traced through time as a point moves away from the origin at constant speed and as the coordinate system rotates at a constant angular speed. Another result, appealing in its simplicity, was Archimedes’ discovery that a sphere circumscribed within a cylinder of the same radius has a volume and area equal to 2/3 of the volume and area of the circumscribing cylinder. Archimedes was so pleased with this result that he requested that a bronze sphere inside a cylinder be placed on his grave.

ARCHIMEDES OF CYRACUS

According to historical record, Archimedes’ life was cut short while he was trying to prove a geometrical theorem by drawing in the sand. When a Roman soldier approached him, Archimedes cried, “Don’t disturb my circles!” With that, he was promptly killed by a swing of the sword. Despite orders from the Roman general Marcellus that Archimedes’ life should be spared, the great scientist was killed by a Roman soldier during the Siege of Syracuse around 212 BCE. Syracuse had been protected by weapons designed by Archimedes.

Many centuries later Europe revived the work of Eudoxus and Archimedes, culminating with the development of calculus.

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