# The Talents of Archimedes

Terri Melanson

Instructor : Barbara Viola

Fundamentals of Mathematics

February 21, 2011

Archimedes was known for several things, a few were Infinitesimals, Hydraulics’s, levers and two things that were named after him they were Archimedes' Principle and Archimedes' Screw. He was born in c. 287 BC in Syracuse Sicily, he died in c. 212 BC said to be around the age of 75. In his lifetime he had many great works in mathematics, physics, engineering, inventing and he was also and astronomer. He was considered to be one of the greatest mathematicians of all time. He came up with a way to calculate the area under the arch of a parabola. He used the exhaustion method to calculate this and to give a remarkably accurate approximation of pi. He also came up with a system for expressing very large numbers. One of the things he was most famous for was being able to use infinitesimals in a way similar to modern integral calculus. In a piece of work called On the Sphere and Cylinder, he states “that any magnitude when added to itself enough times will exceed any given magnitude.” This was called Archimedean property of real numbers. In another of his works called The Sand Reckoner, he sets out to prove he can calculate the number of grains of sand in the entire universe. He was quoted to say “There are some, King Gelo who think that the number of the sand is infinite in multitude : and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited.” In order to prove this statement he devised a system of counting based on the myriad, which came from the Greek murias for the number 10,000. He concluded that in order to calculate the number of grains of sand it required to fill the universe would be 8 vigintillion or 8 x 10 to the 63rd power.

Archimedes was also famous for his writings, most of his writings had to do with...

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