Archimedes' Mechanical Method
February 17, 2009
Bailey Hall 207
Refreshments will be served at 3:45 in Bailey 204
In 1906, Danish mathematical historian J. L. Heiberg made a remarkable discovery in a convent in Constantinople (now Istanbul). He discovered a 900-year old document written over many times, with remnants of early imperfectly erased writing still visible. Some of the writing was a copy of a much earlier letter written by Archimedes in the third century BC to his friend Eratosthenes (best known today for his very accurate measurement of the circumference of the Earth and for his method of listing primes). This letter contains what has come to be known as Archimedes’ Mechanical Method.
The Mechanical Method uses the Law of the Lever (“Two weights balance at distances from the fulcrum that are inversely proportional to their magnitudes”) to relate areas and volumes of various geometric objects. The technique involves something that looks very much like calculus. We shall present one of Archimedes’ results using his Mechanical Method: A sphere has four times the volume of a cone with base equal to a great circle of the sphere and height equal to its radius.
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