Usefulness of De Moivre's Theorem
Date: 2/10/96 at 10:9:18 From: Anonymous Subject: Use of DeMoivre's Theorem What is the usefulness of DeMoivre's theorem?
Date: 2/10/96 at 12:18:0 From: Doctor Sarah Subject: Re: Use of DeMoivre's Theorem Hello! De Moivre's theorem involves the branch of trigonometry that deals with imaginary quantities. Here's some information found by doing a Web search on de Moivre. It's from a Web page called The English Mathematicians of the Eighteenth Century: _A Short Account of the History of Mathematics_ (4th edition, 1908) by W. W. Rouse Ball. The URL is: http://www.maths.tcd.ie/pub/HistMath/People/18thCentury/RouseBall/RB_Engl18C.html "He is best known for having, together with Lambert, created that part of trigonometry which deals with imaginary quantities. Two theorems on this part of the subject are still connected with his name, namely, that which asserts that sin nx + i cos nx is one of the values of (sin x + i cos x)^n, and that which gives the various quadratic factors of x^(2n) - 2p x^n + 1." Here's something about de Moivre's life: "Demoivre (more correctly written as de Moivre) was born at Vitry on May 26, 1667, and died in London on November 27, 1754. His parents came to England when he was a boy, and his education and friends were alike English. His interest in the higher mathematics is said to have originated in his coming by chance across a copy of Newton's _Principia_. From the eulogy on him delivered in 1754 before the French Academy it would seem that his work as a teacher of mathematics had led him to the house of the Earl of Devonshire at the instant when Newton, who had asked permission to present a copy of his work to the earl, was coming out. Taking up the book, and charmed by the far- reaching conclusions and the apparent simplicity of the reasoning, Demoivre thought nothing would be easier than to master the subject, but to his surprise found that to follow the argument overtaxed his powers. He, however, bought a copy, and as he had but little leisure he tore out the pages in order to carry one or two of them loose in his pocket so that he could study them in the intervals of his work as a teacher. Subsequently he joined the Royal Society, and became intimately connected with Newton, Halley, and other mathematicians of the English school. The manner of his death has a certain interest for psychologists. Shortly before it he declared that it was necessary for him to sleep some ten minutes or a quarter of an hour longer each day than the preceding one. The day after he had thus reached a total of something over twenty-three hours he slept up to the limit of twenty-four hours, and then died in his sleep. "His chief works, other than numerous papers in the _Philosophical Transactions_, were _The Doctrine of Chances_, published in 1718, and the _Miscellanea Analytica_, published in 1730. In the former the theory of recurring series was first given, and the theory of partial fractions which Cotes's premature death had left unfinished was completed, while the rule for finding the probability of a compound event was enunciated. The latter book, besides the trigonometrical propositions mentioned above, contains some theorems in astronomy, but they are treated as problems in analysis." -Doctor Sarah, The Math Forum
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