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Archimedes Lost Book

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Archimedes of Syracuse (c. 287 BC -- c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formula for the volumes of solids of revolution, and an ingenious system for expressing very large numbers.The Archimedes Palimpsest is a palimpsest (ancient overwritten manuscript) on parchment in the form of a codex (hand-written bound book, as opposed to a scroll). It originally was a 10th-century Byzantine copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes. The manuscript currently belongs to an American private collector. The most remarkable of the above works is The Method, of which the palimpsest contains the only known copy.In his other works, Archimedes often proves the equality of two areas or volumes with Eudoxus' method of exhaustion, an ancient Greek counterpart of the modern method of limits. Since the Greeks were aware that some numbers were irrational, their notion of a real number was a quantity Q approximated by two sequences, one providing an upper bound and the other a lower bound. If you find two sequences U and L, with U always bigger than Q, and L always smaller than Q, and if the two sequences eventually came closer together than any respecified amount, then Q is found, or exhausted, by U and L.Directed and Produced by Liz Tucker.From Nova Series

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