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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. 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 theory. Life Early years Abraham ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academy Of Saumur
The Academy of Saumur (french: Académie de Saumur) was a Huguenot university at Saumur in western France. It existed from 1593, when it was founded by Philippe de Mornay, until shortly after 1685, when Louis XIV decided on the revocation of the Edict of Nantes, ending the limited toleration of Protestantism in France. Amyraldism The Academy was the home of Amyraldism, an important strand of Protestant thought of the seventeenth century. Also called Saumurianism or hypothetical universalism, it was a moderate Calvinist movement, remaining within Calvinism. The Helvetic Consensus and Westminster Confession were concerned to combat the tendency Amyraldism represented. Faculty Students See also * List of early modern universities in Europe The list of early modern universities in Europe comprises all universities that existed in the early modern age (1501–1800) in Europe. It also includes short-lived foundations and educational institutions whose university status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Moivre's Law
De Moivre's Law is a survival model applied in actuarial science, named for Abraham de Moivre. It is a simple law of mortality based on a linear survival function. Definition De Moivre's law has a single parameter \omega called the ''ultimate age''. Under de Moivre's law, a newborn has probability of surviving at least ''x'' years given by the survival function : S(x) = 1 - \frac, \qquad 0 \leq x < \omega. In ''(x)'' denotes a status or life that has survived to age ''x'', and ''T''(''x'') is the future lifetime of ''(x)'' (''T''(''x'') is a random variable). The that ''(x)'' survives to age ''x+t'' is ''Pr [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vitry-le-François
Vitry-le-François () is a commune in the Marne department in northeastern France. It is located on the river Marne and is the western terminus of the Marne–Rhine Canal. Vitry-le-François station has rail connections to Paris, Reims, Strasbourg, Metz, Dijon and several regional destinations. History The present town is a relatively recent construction, having been built in 1545 at the behest of King Francis who wished to replace, on a new site, Vitry-en-Perthois, which in 1544 had been entirely destroyed as part of the backwash from the king's Italian War of 1542–46. The new Vitry was to be a modern city, constructed according to a plan produced by Girolamo Marini. The king's role in its creation resulted in Vitry-le-François receiving the king's name as part of its own name. At the beginning of World War I in August 1914, Joseph Joffre established the Grand Quartier Général at the Place Royer-Collard. Demography Features * Its church of Notre-Dame is a 17t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huguenot
The Huguenots ( , also , ) were a religious group of French Protestants who held to the Reformed, or Calvinist, tradition of Protestantism. The term, which may be derived from the name of a Swiss political leader, the Genevan burgomaster Bezanson Hugues (1491–1532?), was in common use by the mid-16th century. ''Huguenot'' was frequently used in reference to those of the Reformed Church of France from the time of the Protestant Reformation. By contrast, the Protestant populations of eastern France, in Alsace, Moselle, and Montbéliard, were mainly Lutherans. In his ''Encyclopedia of Protestantism'', Hans Hillerbrand wrote that on the eve of the St. Bartholomew's Day massacre in 1572, the Huguenot community made up as much as 10% of the French population. By 1600, it had declined to 7–8%, and was reduced further late in the century after the return of persecution under Louis XIV, who instituted the '' dragonnades'' to forcibly convert Protestants, and then finally revoke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Champagne (province)
Champagne () was a province in the northeast of the Kingdom of France, now best known as the Champagne wine region for the sparkling white wine that bears its name in modern-day France. The County of Champagne, descended from the early medieval kingdom of Austrasia, passed to the French crown in 1314. Formerly ruled by the counts of Champagne, its western edge is about 160 km (100 miles) east of Paris. The cities of Troyes, Reims, and Épernay are the commercial centers of the area. In 1956, most of Champagne became part of the French administrative region of Champagne-Ardenne, which comprised four departments: Ardennes, Aube, Haute-Marne, and Marne. From 1 January 2016, Champagne-Ardenne merged with the adjoining regions of Alsace and Lorraine to form the new region of Grand Est. Etymology The name ''Champagne'', formerly written ''Champaigne'', comes from French meaning "open country" (suited to military maneuvers) and from Latin ''campanius'' meaning "level country" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. 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 general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory. If X_1, X_2, \dots, X_n, \dots are random samples drawn from a population with overall mean \mu and finite variance and if \bar_n is the sample mean of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( or \phi) denotes the golden ratio. The constant \varphi satisfies the quadratic equation \varphi^2 = \varphi + 1 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, and also goes by several 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 construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of \varphi—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Numbers
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :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, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. 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 Fibonacci numbers include co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-form Expression
In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., ''n''th root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions may vary with author and context. Example: roots of polynomials The solutions of any quadratic equation with complex coefficients can be expressed in closed form in terms of addition, subtraction, multiplication, division, and square root extraction, each of which is an elementary function. For example, the quadratic equation :ax^2+bx+c=0, is tractable since its solutions can be expressed as a closed-form expression, i.e. in terms of elementary functions: :x=\frac. Similarly, solutions of cubic and quartic (third and fourth degree) equations can be expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binet's Formula
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :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, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. 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 Fibonacci numbers include co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 for calculating the probabilities 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
