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Gabriel Cramer
Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. Biography Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet. The progenitor of the Cramer family in Geneva was Jean-Ulrich Cramer, Gabriel's great-grandfather, who immigrated from Strasbourg in 1634. Cramer's mother, a member of the Mallet family, was of Huguenot origin. Cramer showed promise in mathematics from an early age. In 1722, aged 18, he received his doctorate from the Academy of Geneva, and at 20 he was made co-chair (along with Jean-Louis Calandrini) of mathematics at the Academy. He became the sole professor of mathematics in 1734 and was appointed professor of philosophy at the Academy in 1750. Cramer was also involved in the politics of the Republic of Geneva, entering first the Council of Two Hundred in 1734 then the Council of Sixty in 1750. He was a member of the science academies of Bologna, Lyon, and Montpellier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geneva
Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the capital of the Canton of Geneva, Republic and Canton of Geneva, and a centre for international diplomacy. Geneva hosts the highest number of International organization, international organizations in the world, and has been referred to as the world's most compact metropolis and the "Peace Capital". Geneva is a global city, an international financial centre, and a worldwide centre for diplomacy hosting the highest number of international organizations in the world, including the headquarters of many agencies of the United Nations and the International Committee of the Red Cross, ICRC and International Federation of Red Cross and Red Crescent Societies, IFRC of the International Red Cross and Red Crescent Movement, Red Cross. In the aftermath ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academy Of Lyon
__NOTOC__ The Academy of Sciences, Humanities and Arts of Lyon (French: Académie des Sciences, Belles-Lettres et Arts de Lyon) is a French learned society founded in 1700. Its founders included: * Claude Brossette, lawyer, alderman of Lyons, and administrator of the Hôtel-Dieu de Lyon; * , President of the Cour des monnaies; * , future consulting physician of King Louis XIV LouisXIV (Louis-Dieudonné; 5 September 16381 September 1715), also known as Louis the Great () or the Sun King (), was King of France from 1643 until his death in 1715. His verified reign of 72 years and 110 days is the List of longest-reign ... and member of the ; * Antoine de Serre, adviser to the Cour des monnaies; * , naturalist; * Father Jean de Saint-Bonnet, professor at the Collège-lycée Ampère. * Thomas Bernard Fellon. Notable Members * Joseph D'Aquin * Jean Pouilloux See also * French art salons and academies Notes References National academies Learned societies of France ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determinant (mathematics)
In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism. However, if the determinant is zero, the matrix is referred to as singular, meaning it does not have an inverse. The determinant is completely determined by the two following properties: the determinant of a product of matrices is the product of their determinants, and the determinant of a triangular matrix is the product of its diagonal entries. 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 an matrix can be define ... [...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 (mathematics), 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 (mathematics), pencil of cubics does, and the points satisfy additional properties; see Cayley–B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Apsides
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the ''apogee'', and at the nearest point the ''perigee'', like with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named ''aphelion'' for the farthest and ''perihelion'' for the nearest point in a heliocentric orbit. Earth's two apsides are the farthest point, ''aphelion'', and the nearest point, ''perihelion'', of its orbit around the host Sun. The terms ''aphelion'' and ''perihelion'' apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planet
A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets by the most restrictive definition of the term: the terrestrial planets Mercury (planet), Mercury, Venus, Earth, and Mars, and the giant planets Jupiter, Saturn, Uranus, and Neptune. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young protostar orbited by a protoplanetary disk. Planets grow in this disk by the gradual accumulation of material driven by gravity, a process called accretion (astrophysics), accretion. The word ''planet'' comes from the Greek () . In Classical antiquity, antiquity, this word referred to the Sun, Moon, and five points of light visible to the naked eye that moved across the background of the stars—namely, Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Family
The Bernoulli family ( ; ; ) of Basel was a Patrician (post-Roman Europe), patrician family, notable for having produced eight mathematically gifted academics who, among them, contributed substantially to the development of mathematics and physics during the Early Modern Switzerland, early modern period. History Originally from Antwerp, a branch of the family relocated to Basel in 1620. While their origin in Antwerp is certain, proposed earlier connections with the Dutch family of Italian ancestry called ''Bornouilla'' (''Bernoullie''), or with the Castilian family ''de Bernuy'' (''Bernoille'', ''Bernouille''), are uncertain. The first known member of the family was Leon Bernoulli (d. 1561), a doctor in Antwerp, at that time part of the Spanish Netherlands. His son, Jacob, emigrated to Frankfurt am Main in 1570 to escape from the Inquisition in the Netherlands, Spanish persecution of the Protestants. Jacob's grandson, a spice trader, also named Jacob, moved to Basel, Switzerlan ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenization of a polynomial, homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation can be restricted to the affine algebraic plane curve of equation . These two operations are each inverse function, inverse to the other; therefore, the phrase algebraic plane curve is often used without specifying explicitly whether it is the affine or the projective case that is considered. If the defining polynomial of a plane algebraic curve is irreducible polynomial, irreducible, then one has an ''irreducible plane algebraic curve''. Otherwise, the algebraic curve is the union of one or several irreducible curves, called its ''Irreduc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Bernoulli
Daniel Bernoulli ( ; ; – 27 March 1782) was a Swiss people, Swiss-France, French mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. His name is commemorated in the Bernoulli's principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the aeroplane wing. Early life Daniel Bernoulli was born in Groningen (city), Groningen, in the Netherlands, into a Bernoulli family, family of distinguished mathematicians.Murray Rothbard, Rothbard, MurrayDaniel Bernoulli and the Founding of Mathematical Economics, ''Mises Institute'' (excerpted from ''An Austrian Perspective on the History of Economic Thought'') The Bernou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Utility Hypothesis
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is U(p)=\sum u(x_k)p_k where p_k is the probability that outcome indexed by k with payoff x_k is realized, and function ''u'' expresses the utility of each respective payoff. Graphically the curvature of the u function captures the agent's risk attitude. For example, imagine you’re offered a choice between receiving $50 for sure, or flipping a coin to win $100 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
