Archimedes

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.

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