Essay/Term paper: Archimedes

Essay, term paper, research paper:  Political Science

Few certain details remain about the life of

antiquity"s greatest mathematician, Archimedes. We know

he was born in 287 B.C.E. around Syracuse from a report

about 1400 years after the fact. Archimedes tells about his

father, Pheidias, in his book The Sandreckoner. Pheidias

was an astronomer, who was famous for being the author of

a treatise on the diameters of the sun and the moon.

Historians speculate that Pheidias" profession explains why

Archimedes chose his career. Some scholars have

characterized Archimedes as an aristocrat who actively

participated in the Syracusan court and may have been

related to the ruler of Syracuse, King Hieron II. We also

know Archimedes died in 212 B.C.E. at the age of 75 in

Syracuse. It is said that he was killed by a Roman soldier,

who was offended by Achimedes, while the Romans seized

Syracuse. Archimedes had a wide variety of interests, which

included encompassing statics, hydrostatics, optics,

astronomy, engineering, geometry, and arithmetic.

Archimedes had more stories passed down through history

about his clever inventions than his mathematical theorems.

This is believed to be so because the average mind of that

period would have no interest in the Archimedean spiral, but

would pay attention to an invention that could move the

earth. Archimedes" most famous story is attributed to a

Roman architect under Emperor Augustus, named Vitruvius.

Vitruvius asked Archimedes to devise some way to test the

weight of a gold wreath. Archimedes was unsuccessful until

one day as he entered a full bath, he noticed that the deeper

he submerged into the tub, the more water flowed out of the

tub. This made him realize that the amount of water that

flowed out of the tub was equal to the volume of the object

being submerged. Therefore by putting the wreath into the

water, he could tell by the rise in water level the volume of

the wreath, despite its irregular shape. This discovery

marked the Law of Hydrostatics, which states that a body

immersed in fluid loses weight equal to the weight of the

amount of fluid it displaces. There are three main mechanical

inventions credited to Archimedes. The first one is the

Archimedean screw which supposedly could serve as a

water pump. The second invention was the compound

pulley. The third invention was the way of finding the volume

of something by displacement as demonstrated in the story

above. Most historians would agree that more important

than his great mechanical inventions were his mathematical

discoveries. The mathematical works that have been

presented to us by Archimedes could be classified into three

groups. The first group consists of works that have as their

major objective the proof of theorems relative to the areas

and volumes of figures bounded by curved lines and

surfaces. The second category contains works that lead to a

geometrical analysis of statical and hydrostatical problems

and the use of statics in geometry. Miscellaneous

mathematical works make up the third group. Toward the

end of Archimedes life, the political situation around him

became worse as the years went by. After the death of

Hieron II, Syracuse fell into the hands of his grandson,

Hieronymus, who changed from the alliance of Rome to the

alliance of Carthage. After the Romans heard of this

revelation they sent a fleet of ships to capture Syracuse.

Archimedes was a key factor to the Syracusians" ability to

hold off the Romans for so long. He is said to have created

catapults to hurl rocks and used compound pulleys with giant

hooks to rip the Roman ships apart. The most well known

invention to ward off the Romans was the construction of a

series of giant lenses used to magnify the sun"s rays and set

Roman ships a blaze. The theorems that Archimedes

discovered and worked on raised Greek mathematics to a

whole new level. He undertook difficult problems in both

mechanics and mathematics with great preserverence.

Archimedes" theorems, postulates, and inventions are still

part of society today. These are some of the reasons that

some scolars rank him with the greatest mathematicians in

history.