Van Ceulen worked himself to death on this computation, at which point the 35 places he had calculated were inscribed on his tombstone. In honor of this poor man, Germany still refers to ? as the Ludolphian number sometimes. In 1593, fourteen years after his polygon attempts, Francois Vieta discovered the first non-geometrical method for finding pi, in the form of an infinite continued product involving ? and the square root of ?...
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By the middle of the 17th century, infinite processes like Vieta's began to dominate the pi-computing field. The simplest series of all was given by Leibniz in 1682, (?/4) = 1 ? 1/3 + 1/5 ? 1/7 + ? Predating Leibniz' series was the discovery by James Gregory in 1670. Leibniz' series is just a special case of this series, which was probably the most important series in the history of ?: arctan x = x ? (x3/3) + (x5/5) ? (x7/7) + ? Next, John Machin arrived on the scene...
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Homer His Life And His Works His second epic is the Odyssey, which tells the story of a great hero Odysseus, and the adventures he embarks on. Tradition has it that he lived in the 12th century BC, around the time of the Trojan War, in an Ionic settlement, either Chios or Smyrna, where he made his living as a court singer and storyteller...	4 / 1014
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