Archimedes

(Eves)

Archimedes

Born: 287 BC in Syracuse, Sicily

died: 212 BC in Syracuse

Archimedes, who combined a genius for mathematics with a physical insight, must rank with Newton, who lived nearly two thousand years later, as one of the founders of mathematical physics.

He is one of the greatest mathematicians of all time. He discovered the Method of Exhaustion – integration, and "Eureka" -- the first law of hydrostatics. Also discovered the laws of levers and used pulleys. His mechanical inventions defeated the Roman fleet of Marcellus.

Archimedes was an aristocrat, the son of an astronomer, but little is known of his early life except that he studied for a time in Alexandria, Egypt. Several of his books were preserved by the Greeks and Arabs into the middle Ages, and, fortunately, the Roman historian Plutarch described a few episodes from his life. In many areas of mathematics as well as in hydrostatics and statics, his work and results were not surpassed for over 1500 years.

He approximated the area of circles (and the value of ¼) by summing the areas of inscribed and circumscribed rectangles, and generalized this "method of exhaustion," by taking smaller and smaller rectangular areas and summing them, to find the areas and even volumes of several other shapes. This anticipated the results of the calculus of Newton and Leibniz by almost 2000 years!

He found the area and tangents to the curve traced by a point moving with uniform speed along a straight line which is revolving with uniform angular speed about a fixed point. This curve, described by r = a in polar coordinates, is now called the "spiral of Archimedes." With calculus it is an easy problem; without calculus it is very difficult.

The king of Syracuse once asked Archimedes to find a way of determining if one of his crowns was pure gold without destroying the crown in the process. The crown weighed the correct amount but that was not a guarantee that it was pure gold. The story is told that as...