Abraham de Moivre (26 May 1667 - 27 November 1754) was a French mathematician known for de Moivre's formula, one of those that link complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was a friend of Isaac Newton,Edmund Halley, and James Stirling. Among his fellow Huguenot exiles inEngland, he was a colleague of the editor and translator Pierre des Maizeaux.
De Moivre wrote a book on probability theory, The Doctrine of Chances, said to have been prized by gamblers. De Moivre first discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the nth power of the golden ratio φ to the nth Fibonacci number.
Abraham de Moivre was born in Vitry in Champagne on May 26, 1667. His father, Daniel de Moivre, was a surgeon who, though middle class, believed in the value of education. He first attended Christian Brothers' Catholic school in Vitry. When he was eleven, his parents sent him to the Protestant Academy at Sedan, where he spent four years studying Greek under Jacques du Rondel.
In 1682 the Protestant Academy at Sedan was suppressed, and de Moivre enrolled to study logic at Saumur for two years. Although mathematics was not part of his course work, de Moivre read several works on mathematics on his own including Elements de Mathematiques by Father Prestet and a short treatise on games of chance, De Ratiociniis in Ludo Aleae, by Christiaan Huygens. In 1684, de Moivre moved to Paris to study physics, and for the first time had formal mathematics training with private lessons from Jacques Ozanam.
By the time he arrived in London, de Moivre was a competent mathematician with a good knowledge of many of the standard texts. To make a living, de Moivre became a private tutor of mathematics, visiting his pupils or teaching in the coffee houses of London. De Moivre continued his studies of mathematics after visiting the Earl of Devonshire and seeing Newton's recent book, Principia Mathematica. Looking through the book, he realized that it was far deeper than the books that he had studied previously, and he became determined to read and understand it.
However, as he was required to take extended walks around London to travel between his students, de Moivre had little time for study, so he tore pages from the book and carried them around in his pocket to read between lessons. Eventually, de Moivre become so knowledgeable about the material that Newton referred questions to him, saying, "Go to Mr. de Moivre. He knows these things better than I do."
By 1692, de Moivre became friends with Edmond Halley and soon after with Isaac Newton himself. In 1695, Halley communicated de Moivre's first mathematics paper, which arose from his study of fluxions in the Principia Mathematica, to the Royal Society. This paper was published in the Philosophical Transactions that same year. Shortly after publishing this paper, de Moivre also generalized Newton's noteworthy binomial theorem into the multinomial theorem.
The Royal Society became apprised of this method in 1697, and it made de Moivre a member two months later. After de Moivre had been accepted, Halley encouraged him to turn his attention to astronomy. In 1705, de Moivre discovered, intuitively, that "the centripetal force of any planet is directly related to its distance from the centre of the forces and reciprocally related to the product of the diameter of the evolute and the cube of the perpendicular on the tangent."
In other words, if a planet, M, follows an elliptical orbit around a focus F and has a point P where PM is tangent to the curve and FPM is a right angle so that FP is the perpendicular to the tangent, then the centripetal force at point P is proportional to FM/(R*(FP)3) where R is the radius of the curvature at M. The mathematician Johann Bernoulli proved this formula in 1710.
Throughout his life de Moivre remained poor. It is reported that he was a regular customer of Slaughter's Coffee House, St. Martin's Lane at Cranbourn Street, where he earned a little money from playing chess. De Moivre continued studying the fields of probability and mathematics until his death in 1754 and several additional papers were published after his death. As he grew older, he became increasingly lethargic and needed longer sleeping hours. He noted that he was sleeping an extra 15 minutes each night and correctly calculated the date of his death on the day when the additional sleep time accumulated to 24 hours, November 27, 1754.
De Moivre pioneered the development of analytic geometry and the theory of probability by expanding upon the work of his predecessors, particularly Christiaan Huygens and several members of the Bernoulli family. He also produced the second textbook on probability theory, The Doctrine of Chances: a method of calculating the probabilities of events in play. (The first book about games of chance, Liber de ludo aleae (On Casting the Die), was written by Girolamo Cardano in the 1560s, but it was not published until 1663.)
This book came out in four editions, 1711 in Latin, and in English in 1718, 1738, and 1756. In the later editions of his book, de Moivre included his unpublished result of 1733, which is the first statement of an approximation to the binomial distribution in terms of what we now call the normal or Gaussian function.
However de Moivre is not usually credited with the invention of the normal distribution because he did not identify the curve as a probability density—it was just a function to be integrated. This was the first method of finding the probability of the occurrence of an error of a given size when that error is expressed in terms of the variability of the distribution as a unit, and the first identification of the calculation of probable error. In addition, he applied these theories to gambling problems and actuarial tables.
De Moivre also published an article called "Annuities upon Lives" in which he revealed the normal distribution of the mortality rate over a person’s age. From this he produced a simple formula for approximating the revenue produced by annual payments based on a person’s age. This is similar to the types of formulas used by insurance companies today.
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