Brad Haymond

Ellsworth High School

Calculus Class

December 2001

Archimedes

Archimedes was a Greek mathematician who lived from 287 BC to 212 BC. He was born in Sicily, Syracuse, where he lived his entire life. Archimedes didn’t travel very often, usually staying close to home. However, during one of his visits to Egypt he invented a popular pump known as the Archimedes’ screw, which is still used in many parts of the world. That is just one example of his many contributions he gave to us.

In a time when little was known about mathematics, Archimedes was determined to use what he knew to find out what he didn’t. At that time, the highest numeral known to man was a myriad, or one thousand. Archimedes was not satisfied to use that as his biggest number, so he set out to find a way to produce larger numbers. He first came up with a question: How many grains of sand are there in the universe? His next step was to come up with a system to measure sand. When he had finally solved his question, his answer was a one with 62 zeroes following it. This led him to the discovery of powers (1*10^62).

Most of Archimedes contributions were in geometry. He worked extensively on plane figures and on the areas and volumes of curved surfaces. The "Measurement of the Circle," is one of his most famous accomplishments. He determined the exact value of pi to be between 3 10/71 and 3 1/7. Archimedes was also very proud of his discovery for finding the volume of a sphere. He was able to prove that the volume of a sphere is two-thirds the volume of the smallest cylinder that it can contain. Before Archimedes passed away he requested that a figure of a sphere and a cylinder would be engraved on his tombstone. His methods started the idea for calculus, which was "invented" two thousand years later by Sir Isaac Newton and Gottfried Wilhelm von Leibniz. In fact, many people believe that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation.

Archimedes was also a great engineer of his time as well. He invented numerous principles that are still used today. Some of these formulas include: Archimedes’ principle of buoyancy and the law of the lever. Legend has it that Archimedes discovered his principle of buoyancy, which states that the buoyancy force is equal to the weight of the liquid displaced, while taking a bath, upon which he is believed to have run naked through the streets of Syracuse shouting, "Eureka," which means I have found it!

The respect that Archimedes received from others was not solely because of his mathematical ability. He played a major part in holding off the Roman attackers when they tried to capture Syracuse. He had invented many machines that they used in the war. When the Romans finally able to captured Syracuse, a Roman soldier killed Archimedes, and his body was laid to rest in 212 BC.

Work Cited

http://itech.fgcu.edu/faculty/clindsey/mhf4404/archimedes/archimedes.html

http://tqjunior.thinkquest.org/4116/History/archimedes.htm

http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Archimedes.html