Monday, March 5, 2012

Abraham de Moivre

Abraham de Moivre (26 May 1667 in Vitry-le-François, Champagne, France – 27 November 1754 in London, England; French ) was a French mathematician famous for de Moivre's formula, which links 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 in England, 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 φ to the nth Fibonacci number.

de Moivre's social status in France was a tenuous one. As a practicing Calvinist (Protestant), de Moivre was a member of a small but significant minority in Catholic France known as "Huguenots." The Huguenots were often wealthy or middle-class families who had converted to Protestantism during the prior century and remained in the Catholic country under the protections granted them by the Edict of Nantes. Passed by Henry IV of France in 1698, the Edict had ended France's religious civil wars by granting the minority religious freedom within designated safe areas of the country.

However, French hostility toward the country's Protestant populations remained, mirroring discriminatory policies toward Catholics in neighboring Britain. In October 1685, King Louis XIV revoked the Edict of Nantes, withdrawing royal protections for France's Protestants. De Moivre was imprisoned for roughly one year for practicing Protestantism.

De Moivre's thoughts on probability and games emerged from an existing body of work on games and risk. Notably, it also arose from the increased interest in gambling and games of chance as the urban centers of Europe grew in population and wealth. For this reason, de Moivre was careful to explain in his introduction that the book should be read as a matter of curiosity only for those involved in games of risk, and should also be considered to have applications outside play.

"The Doctrine of Chances" made use of games played during the period to explore the larger patterns formed by random individual events. The law of probability states that the chances of rolling a particular number (a four, for example) on a die with faces one through six is, not surprisingly, one in six (1/6). The same law shows that the probability of two events, such as rolling two fours with two rolls of the dice, may be computed by multiplying the probability of arriving at six in each individual role: 1/6 x 1/6. With each event, the mathematician adds one more probability, in this case 1/6, to the multiplication string.

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