Chapter 7 - 2

02 History

Archimedes

His name is hardly a household word, although the word he yelled in the street after solving a difficult problem “Eureka” is known by many.

Yet, to mathematician Archimedes of the 3rd century, modern people owe their understanding of such fundamental physical phenomena as the principles behind the pulley as well as the fulcrum and lever.

Considered by some to be among the greatest mathematicians of all time, Archimedes perfected a method for measuring the areas, volumes, and surfaces of many bodies.

In his own time, however, he was known best for inventing war machines that helped defend his hometown from attacking Romans.

Archimedes, the son of an astronomer, was born in Syracuse, Sicily, in 287 BCE.

He may have been related to the King of Syracuse, Hiero ll, but in any case, he often ended up applying his mathematical genius to problems and needs set forth by the king.

As a young man, Archimedes studied the teachings of renowned mathematician Euclid in Alexandria, Egypt.

Although he preferred to study mathematics for its own sake, Archimedes was often called upon to apply his knowledge in the defense of Syracuse, which was an object of contention between the great powers of Rome and Carthage.

When the Romans attacked Syracuse in 214 BCE, Archimedes displayed a number of his impressive war machines.

According to witnesses, some of these could sink ships using weights that thrust out of a wall, or lift a ship high by one end, swing it around, then throw it against rocks or to the bottom of the sea.

But the inventor called these “mere amusements in geometry” compared with his complete absorption in solving abstract problems.

Among Archimedes’s practical inventions for the king was a device used to draw rainwater out of a ship using a crank and a spiral.

This method of irrigation is still used today in some countries.

He also found a way to prove his suspicion that a goldsmith had cheated the king in making a crown.

Observing the displacement of water when he got into the bath, Archimedes realized that he could measure the crown’s volume thus and calculate its density to determine whether or not the jeweler had cut the gold with silver.

In fact, he had.

This discovery led Archimedes to run down the street shouting “I found it!” (“Eureka”)

Archimedes left nine books of mathematics that set out the fundamental principles of mechanics using geometry.

His work paved the way for the calculus of the infinite, which was perfected in later centuries.

He was most proud of the work he did showing the relationship between the surface area and volume of a cylinder circumscribing a sphere, and this is what marked his tomb.

So respected was Archimedes that this tribute was ordered by the Roman general who ultimately defeated Syracuse and whose soldier killed the seventy-five-year-old mathematician.

Legend has it that Archimedes was too caught up in a mathematical problem to notice the invading soldier and was struck dead.