Archimedes Essay, Research Paper

Few certain details remain about the life of antiquit^s greatest

mathematician, Archimedes. We know he was born in 287 B.C. 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. 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.

318