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Gabriel Cramer
Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. He was the son of physician Jean Cramer and Anne Mallet Cramer. Biography Cramer showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chairHe did not get the chair of philosophy he had been a candidate for; but the University of Geneva was so impressed by him that it created a chair of mathematics for him and for his friend Jean-Louis Calandrini; the two alternated as chairs. of mathematics at the University of Geneva. In 1728 he proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli. He published his best-known work in his forties. This included his treatise on algebraic curves (1750). It contains the earliest demonstration that a curve of the ''n''-th degree is determined by ''n''(''n'' + 3)/2 points on it, in general position. (See Cramer's theorem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Gardelle
Robert Gardelle (1682-1766) was a Swiss artist, engraver and etcher born in Geneva, then in the Republic of Geneva. Gardelle studied under Largillière in Paris, where he distinguished himself as a portrait painter, producing also etchings of portraits and of views of Geneva. Gardelle is known for both the quantity of portraits he produced and the speed with which he produced them; Cambridge University Library noted during a 1978 exhibition that Gardelle was prolific and "often painted portraits in two or three days." References Further reading * Dagmar Böcker: Gardelle, Robert'. In: Historisches Lexikon der Schweiz The ''Historical Dictionary of Switzerland'' is an encyclopedia on the history of Switzerland that aims to take into account the results of modern historical research in a manner accessible to a broader audience. The encyclopedia is publish ... * Auguste Bouvier: ''Quatre vues de Genève peintes par Robert Gardelle'', Genève 1931 * Waldemar Deonna: ''Le pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Position
In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the ''general case'' situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differs in different settings. For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident). One also says "two generic lines intersect in a point", which is formalized by the notion of a generic point. Similarly, three generic points in the plane are not collinear; if three points are collinear (even stronger, if two coincide), this is a degenerate case. This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating general theorems or giving precise statements thereof, and when writing computer programs (see '' generic compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
18th-century Scientists From The Republic Of Geneva
The 18th century lasted from January 1, 1701 ( MDCCI) to December 31, 1800 ( MDCCC). During the 18th century, elements of Enlightenment thinking culminated in the American, French, and Haitian Revolutions. During the century, slave trading and human trafficking expanded across the shores of the Atlantic, while declining in Russia, China, and Korea. Revolutions began to challenge the legitimacy of monarchical and aristocratic power structures, including the structures and beliefs that supported slavery. The Industrial Revolution began during mid-century, leading to radical changes in human society and the environment. Western historians have occasionally defined the 18th century otherwise for the purposes of their work. For example, the "short" 18th century may be defined as 1715–1789, denoting the period of time between the death of Louis XIV of France and the start of the French Revolution, with an emphasis on directly interconnected events. To historians who expand the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1752 Deaths
Year 175 ( CLXXV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Piso and Iulianus (or, less frequently, year 928 ''Ab urbe condita''). The denomination 175 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Marcus Aurelius suppresses a revolt of Avidius Cassius, governor of Syria, after the latter proclaims himself emperor. * Avidius Cassius fails in seeking support for his rebellion and is assassinated by Roman officers. They send his head to Aurelius, who persuades the Senate to pardon Cassius's family. * Commodus, son of Marcus Aurelius and his wife Faustina, is named Caesar. * M. Sattonius Iucundus, decurio in Colonia Ulpia Traiana, restores the Thermae of Coriovallum (modern Heerlen) there are sources that state this happe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1704 Births
Seventeen or 17 may refer to: *17 (number), the natural number following 16 and preceding 18 * one of the years 17 BC, AD 17, 1917, 2017 Literature Magazines * ''Seventeen'' (American magazine), an American magazine * ''Seventeen'' (Japanese magazine), a Japanese magazine Novels * ''Seventeen'' (Tarkington novel), a 1916 novel by Booth Tarkington *''Seventeen'' (''Sebuntiin''), a 1961 novel by Kenzaburō Ōe * ''Seventeen'' (Serafin novel), a 2004 novel by Shan Serafin Stage and screen Film * ''Seventeen'' (1916 film), an American silent comedy film *''Number Seventeen'', a 1932 film directed by Alfred Hitchcock * ''Seventeen'' (1940 film), an American comedy film *''Eric Soya's '17''' (Danish: ''Sytten''), a 1965 Danish comedy film * ''Seventeen'' (1985 film), a documentary film * ''17 Again'' (film), a 2009 film whose working title was ''17'' * ''Seventeen'' (2019 film), a Spanish drama film Television * ''Seventeen'' (TV drama), a 1994 UK dramatic short starring Christ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Devil's Curve
In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form : y^2(y^2 - b^2) = x^2(x^2 - a^2). The polar equation of this curve is of the form :r = \sqrt = \sqrt. Devil's curves were discovered in 1750 by Gabriel Cramer, who studied them extensively. The name comes from the shape its central lemniscate takes when graphed. The shape is named after the juggling game diabolo The diabolo ( ; commonly misspelled ''diablo'') is a juggling or circus prop consisting of an axle () and two cups (hourglass/egg timer shaped) or discs derived from the Chinese yo-yo. This object is spun using a string attached to two hand ..., which was named after the Devil and which involves two sticks, a string, and a spinning prop in the likeness of the lemniscate. For , b, , a, it is vertical. Is , b, = , a, , the shape becomes a circle. The vertical hourglass intersects the y-axis at b,-b, 0 . The horizonta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cramer–Castillon Problem
In geometry, the Cramer–Castillon problem is a problem stated by the Swiss mathematician Gabriel Cramer solved by the Italian mathematician, resident in Berlin, Jean de Castillon in 1776. The problem consists of (see the image): Given a circle Z and three points A, B, C in the same plane and not on Z, to construct every possible triangle inscribed in Z whose sides (or their elongations) pass through A, B, C respectively. Centuries before, Pappus of Alexandria had solved a special case: when the three points are collinear. But the general case had the reputation of being very difficult. After the geometrical construction of Castillon, Lagrange found an analytic solution, easier than Castillon's. In the beginning of the 19th century, Lazare Carnot Lazare Nicolas Marguerite, Count Carnot (; 13 May 1753 – 2 August 1823) was a French mathematician, physicist and politician. He was known as the "Organizer of Victory" in the French Revolutionary Wars and Napoleonic Wars. Educa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cramer - Introduction A L'analyse Des Lignes Courbes Algebriques, 1750 - 1262149
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Cramer may refer to: Businesses * Cramer brothers, 18th century publishers * Cramer Systems, a software company * Cramer & Co., a former musical-related business in London Other uses * Cramer (surname), including a list of people and fictional characters * Cramer, Minnesota, United States, an unincorporated community * Mount Cramer, Idaho, United States See also * * * Kramer (other) Kramer is a Dutch-language, Dutch and Low German word for a small merchant, hawker, or retailer and is a common occupational surname. The word may refer to: People * Kramer (surname) * Kramer (musician), a musician and record producer * Cosmo Kra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determinant (mathematics)
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix is denoted , , or . The determinant of a matrix is :\begin a & b\\c & d \end=ad-bc, and the determinant of a matrix is : \begin a & b & c \\ d & e & f \\ g & h & i \end= aei + bfg + cdh - ceg - bdi - afh. The determinant of a matrix can be defined in several equivalent ways. Leibniz formula expresses the determinant as a sum of signed products of matrix entries such that each summand is the product of different entries, and the number of these summands is n!, the factorial of (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Curve
In mathematics, a cubic plane curve is a plane algebraic curve defined by a cubic equation : applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation. Here is a non-zero linear combination of the third-degree monomials : These are ten in number; therefore the cubic curves form a projective space of dimension 9, over any given field . Each point imposes a single linear condition on , if we ask that pass through . Therefore, we can find some cubic curve through any nine given points, which may be degenerate, and may not be unique, but will be unique and non-degenerate if the points are in general position; compare to two points determining a line and how five points determine a conic. If two cubics pass through a given set of nine points, then in fact a pencil of cubics does, and the points satisfy additional properties; see Cayley–Bacharach theorem. A cubic curve may have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus. In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
