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In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n it is the case that ( + ) = + , where i is the imaginary unit (i 2 = −1).
According to the de Moivre–Laplace theorem, as n grows large, the shape of the discrete distribution converges to the continuous Gaussian curve of the normal distribution. In probability theory , the de Moivre–Laplace theorem , which is a special case of the central limit theorem , states that the normal distribution may be used as an ...
Thébault's theorem ; Theorem of de Moivre–Laplace (probability theory) Theorem of the cube (algebraic varieties) Theorem of the gnomon ; Theorem of three moments ; Theorem on friends and strangers (Ramsey theory) Thévenin's theorem (electrical circuits) Thompson transitivity theorem (finite groups)
de Moivre's theorem may be: de Moivre's formula, a trigonometric identity; Theorem of de Moivre–Laplace, a central limit theorem This page was last edited on 28 ...
Published in 1738 by Woodfall and running for 258 pages, the second edition of de Moivre's book introduced the concept of normal distributions as approximations to binomial distributions. In effect de Moivre proved a special case of the central limit theorem. Sometimes his result is called the theorem of de Moivre–Laplace.
de Moivre's illustration of his piecewise linear approximation. De Moivre's law first appeared in his 1725 Annuities upon Lives, the earliest known example of an actuarial textbook. [6] Despite the name now given to it, de Moivre himself did not consider his law (he called it a "hypothesis") to be a true description of the pattern of human ...
De Moivre's most notable achievement in probability was the discovery of the first instance of central limit theorem, by which he was able to approximate the binomial distribution with the normal distribution. [16]
De Moivre–Laplace theorem; Lyapunov's central limit theorem; Misconceptions about the normal distribution; Martingale central limit theorem; Infinite divisibility (probability) Method of moments (probability theory) Stability (probability) Stein's lemma; Characteristic function (probability theory) Lévy continuity theorem; Darmois ...