Abraham De Moivre
Abraham de Moivre FRS (; 26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He moved to England at a young age due to the religious persecution of Huguenots in France which reached a climax in 1685 with the Edict of Fontainebleau. He was a friend of Isaac Newton, Edmond Halley, and James Stirling (mathematician), 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 ''n''th power of the golden ratio ''φ'' to the ''n''th Fibonacci number. He also was the first to postulate the central limit theorem, a cornerstone of probability theo ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Joseph Highmore
Joseph Highmore (13 June 16923 March 1780) was an English painter of Portrait painting, portraits, conversation pieces and History painting, history subjects, illustrator and author. After retiring from his career as a painter at the age of 70, he published art historical and critical articles.West, S. ''Highmore, Joseph'' Grove Art Online. Retrieved 18 March 2022 Life Highmore was born on 13 June 1692, in London, the third son of Edward Highmore, a coal merchant, and nephew of Thomas Highmore, Serjeant Painter to William III of England, William III. He displayed early his ability in art but was discouraged by his family from taking up art professionally, and began a legal training instead. At the ending of ...[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Central Limit Theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distribution, standard normal distribution. This holds even if the original variables themselves are not Normal distribution, normally distributed. There are several versions of the CLT, each applying in the context of different conditions. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated as late as 1920. In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a Sampling ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \frac = \frac = \varphi, where the Greek letter Phi (letter), phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli; it also goes by other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the Straightedge and compass construction, construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has bee ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Fibonacci Numbers
In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The Fibonacci numbers were first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the '' Fibonacci Quarterly''. Applications of Fibon ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Closed-form Expression
In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. Commonly, the basic functions that are allowed in closed forms are ''n''th root, exponential function, logarithm, and trigonometric functions. However, the set of basic functions depends on the context. For example, if one adds polynomial roots to the basic functions, the functions that have a closed form are called elementary functions. The ''closed-form problem'' arises when new ways are introduced for specifying mathematical objects, such as limits, series, and integrals: given an object specified with such tools, a natural problem is to find, if possible, a ''closed-form expression'' of this object; that is, an expression of this object in terms of previous ways of specifying it. Example: roots of polynomials The quadratic ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Binet's Formula
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The Fibonacci numbers were first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Appli ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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The Doctrine Of Chances
''The Doctrine of Chances'' was the first textbook on probability theory, written by 18th-century French mathematician Abraham de Moivre and first published in 1718.. De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots. The book's title came to be synonymous with ''probability theory'', and accordingly the phrase was used in Thomas Bayes' famous posthumous paper ''An Essay Towards Solving a Problem in the Doctrine of Chances'', wherein a version of Bayes' theorem was first introduced. Editions The full title of the first edition was ''The Doctrine of Chances: or, A Method of Calculating the Probability of Events in Play''. It was published in 1718, by W. Pearson, and ran for 175 pages. 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 spec ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Pierre Des Maizeaux
Pierre des Maizeaux, also spelled Desmaizeaux (c. 1666 or 1673June 1745), was a French Huguenot writer exiled in London, best known as the translator and biographer of Pierre Bayle. He was born in Pailhat, Auvergne, France. His father, a minister of the reformed church, had to leave France on the revocation of the Edict of Nantes, and took refuge in Geneva, where Pierre was educated. Pierre Bayle gave him an introduction to Anthony Ashley-Cooper, 3rd Earl of Shaftesbury, with whom, in 1689, he went to England, where he engaged in literary work. He remained in close touch with the religious refugees in England and Holland, and through his involvement with the Huguenot information centre based at the masonic Rainbow Coffee House he was constantly in correspondence with the leading continental savants and writers, who were in the habit of employing him to conduct such business as they might have in England. In 1720 he was elected a fellow of the Royal Society. He was a colleague of ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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James Stirling (mathematician)
James Stirling (11 May Old Style and New Style dates, O.S. 1692, Garden, Stirlingshire – 5 December 1770, Edinburgh) was a Scotland, Scottish mathematician. He was nicknamed "The Venetian". The Stirling numbers, Stirling permutations, and Stirling's approximation are named after him. He also proved the correctness of Isaac Newton's classification of cubic plane curves. Biography Stirling was born on 11 May 1692 Old Style and New Style dates, O.S. at Garden House near Stirling, the third son of Archibald Stirling (1651-1715) and Anna Hamilton, and grandson of Archibald Stirling, Lord Garden, (1617-1668). At 18 years of age he went to Balliol College, Oxford, where, chiefly through the influence of the John Erskine, Earl of Mar (1675–1732), Earl of Mar, he was nominated in 1711 to be one of Bishop Warner's exhibitioners (or Snell exhibitioner) at Balliol. In 1715 he was expelled on account of his correspondence with his cousins, who were members of the Keir and Garden fami ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Edmond Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720. From an observatory he constructed on Saint Helena in 1676–77, Halley catalogued the southern celestial hemisphere and recorded a transit of Mercury across the Sun. He realised that a similar transit of Venus could be used to determine the distances between Earth, Venus, and the Sun. Upon his return to England, he was made a fellow of the Royal Society, and with the help of King Charles II of England, Charles II, was granted a master's degree from University of Oxford, Oxford. Halley encouraged and helped fund the publication of Isaac Newton's influential ''Philosophiæ Naturalis Principia Mathematica'' (1687). From observations Halley made in September 1682, he used Newton's law of universal gravitation to compute the periodicity of Halley's Comet in his 1705 ''Synopsis of the Astronomy of Comets''. It ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Isaac Newton
Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, achieved the Unification of theories in physics#Unification of gravity and astronomy, first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and Leibniz–Newton calculus controversy, shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating calculus, infinitesimal calculus, though he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science. In the , Newton formulated the Newton's laws of motion, laws of motion and Newton's law of universal g ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |