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Pierre Frédéric Sarrus
Pierre Frédéric Sarrus (; 10 March 1798, Saint-Affrique – 20 November 1861) was a French mathematician. Sarrus was a professor at the University of Strasbourg, France (1826–1856) and a member of the French Academy of Sciences in Paris (1842). He is the author of several treatises, including one on the solution of numeric equations with multiple unknowns (1842); one on multiple integrals and their integrability conditions; and one on the determination of the orbits of the comets. Sarrus discovered a mnemonic rule for solving the determinant of a 3-by-3 matrix, named Sarrus' scheme. He also demonstrated the fundamental lemma of the calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f .... Additionally, he also developed the Sarrus linkage, the first linkag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint-Affrique
Saint-Affrique (; Languedocien: ''Sant Africa'') is a commune in the Aveyron department in Southern France. History Saint-Affrique grew in the 6th century around the tomb of St. Africain, bishop of Comminges. In the 12th century a fortress was built on the neighboring rock of Caylus. The possession of Saint-Affrique was vigorously contested during the French Wars of Religion. It was eventually occupied by the Huguenots until 1629, when it was seized and dismantled by a royal army. Geography The Sorgues, a tributary of the Dourdou de Camarès, flows through the commune and crosses the town. The Dourdou de Camarès flows northwestward through the western part of the commune and forms part of its northwestern border. Population Sights An old bridge over the Sorgue and some megaliths in the neighborhood, especially, the dolmen of Tiergues, are of antiquarian interest. Personalities Saint-Affrique was the birthplace of: * Pierre Frédéric Sarrus (1798–1861), mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Sarrus
In matrix theory, the rule of Sarrus is a mnemonic device for computing the determinant of a 3 \times 3 matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ... named after the French mathematician Pierre Frédéric Sarrus. Consider a 3 \times 3 matrix :M=\begina&b&c\\d&e&f\\g&h&i\end then its determinant can be computed by the following scheme. Write out the first two columns of the matrix to the right of the third column, giving five columns in a row. Then add the products of the diagonals going from top to bottom (solid) and subtract the products of the diagonals going from bottom to top (dashed). This yieldsPaul Cohn: ''Elements of Linear Algebra''. CRC Press, 1994, p. 69/ref> : \begin \det(M)= \begin a&b&c\\d&e&f\\g&h&i \end= aei + bfg + cdh - gec - hfa - idb . \end ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Saint-Affrique
The term "the people" refers to the public or common mass of people of a polity. As such it is a concept of human rights law, international law as well as constitutional law, particularly used for claims of popular sovereignty. In contrast, a people is any plurality of persons considered as a whole. Used in politics and law, the term "a people" refers to the collective or community of an ethnic group or nation. Concepts Legal Chapter One, Article One of the Charter of the United Nations states that "peoples" have the right to self-determination. Though the mere status as peoples and the right to self-determination, as for example in the case of Indigenous peoples (''peoples'', as in all groups of indigenous people, not merely all indigenous persons as in ''indigenous people''), does not automatically provide for independent sovereignty and therefore secession. Indeed, judge Ivor Jennings identified the inherent problems in the right of "peoples" to self-determination, as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1861 Deaths
This year saw significant progress in the Unification of Italy, the outbreak of the American Civil War, and the emancipation reform abolishing serfdom in the Russian Empire. Events January * January 1 ** Benito Juárez captures Mexico City. ** The first steam-powered carousel is recorded, in Bolton, England. * January 2 – Friedrich Wilhelm IV of Prussia dies, and is succeeded by Wilhelm I. American Civil War: ** January 3 – Delaware votes not to secede from the Union. ** January 9 – Mississippi becomes the second state to secede from the Union. ** January 10 – Florida secedes from the Union. ** January 11 – Alabama secedes from the Union. ** January 12 – Major Robert Anderson sends dispatches to Washington. ** January 19 – Georgia secedes from the Union. ** January 21 – Jefferson Davis resigns from the United States Senate. ** January 26 – Louisiana secedes from the Union. * January 29 – Kansas is adm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1798 Births
Events January–June * January – Eli Whitney contracts with the U.S. federal government for 10,000 muskets, which he produces with interchangeable parts. * January 4 – Constantine Hangerli enters Bucharest, as Prince of Wallachia. * January 22 – A coup d'état is staged in the Netherlands (Batavian Republic). Unitarian Democrat Pieter Vreede ends the power of the parliament (with a conservative-moderate majority). * February 10 – The Pope is taken captive, and the Papacy is removed from power, by French General Louis-Alexandre Berthier. * February 15 – U.S. Representative Roger Griswold (Fed-CT) beats Congressman Matthew Lyon (Dem-Rep-VT) with a cane after the House declines to censure Lyon earlier spitting in Griswold's face; the House declines to discipline either man.''Harper's Encyclopaedia of United States History from 458 A. D. to 1909'', ed. by Benson John Lossing and, Woodrow Wilson (Harper & Brothers, 1910) p171 * March &ndash ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat Pseudoprime
In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Definition Fermat's little theorem states that if p is prime and a is coprime to p, then a^-1 is divisible by p. For a positive integer a, if a composite integer x divides a^-1 then x is called a Fermat pseudoprime to base a. In other words, a composite integer is a Fermat pseudoprime to base a if it successfully passes the Fermat primality test for the base a. The false statement that all numbers that pass the Fermat primality test for base 2 are prime is called the Chinese hypothesis. The smallest base-2 Fermat pseudoprime is 341. It is not a prime, since it equals 11·31, but it satisfies Fermat's little theorem: 2^ \equiv 1 (\bmod) and thus passes the Fermat primality test for the base 2. Pseudoprimes to base 2 are sometimes called Sarrus numbers, after P. F. Sarrus who discovered that 341 has this property, Poulet numbers, after P. Poulet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sarrus Linkage
The Sarrus linkage, invented in 1853 by Pierre Frédéric Sarrus, is a mechanical linkage to convert a limited circular motion to a linear motion or vice versa without reference guideways. It is a spatial six-bar linkage (6R) with two groups of three parallel adjacent joint-axes. Although Charles-Nicolas Peaucellier was widely recognized for being the first to invent such a straight-line mechanism, the Sarrus linkage had been invented earlier; however, it was largely unnoticed for a time. – Sarrus' mechanism Description The Sarrus linkage consists of four links in two identical groups that are perpendicular to each other, with all links having equal lengths. In the examples shown, the linkage uses two horizontal plates (cyan ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of functionals: Map (mathematics), mappings from a set of Function (mathematics), functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lemma (mathematics)
In mathematics and other fields, a lemma (: lemmas or lemmata) is a generally minor, proven Theorem#Terminology, proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to mathematical proof, prove; however, a lemma can also turn out to be more important than originally thought. Etymology From the Ancient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus something taken for granted in an argument. Comparison with theorem There is no formal distinction between a lemma and a theorem, only one of intention (see Theorem#Terminology, Theorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a more substantial theorem – a step in the direction of proof. Well-known lemmas Some powerful results in mathematics are known as lemmas, first named for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (: matrices) is a rectangle, rectangular array or table of numbers, symbol (formal), symbols, or expression (mathematics), expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " matrix", or a matrix of dimension . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotation (mathematics), rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French First Republic
In the history of France, the First Republic (), sometimes referred to in historiography as Revolutionary France, and officially the French Republic (), was founded on 21 September 1792 during the French Revolution. The First Republic lasted until the declaration of the First French Empire, First Empire on 18 May 1804 under Napoleon, Napoléon Bonaparte, although the form of government changed several times. On 21 September 1792, the deputies of the Convention, gathered for the first time, unanimously decide the Proclamation of the abolition of the monarchy, abolition of the constitutional monarchy in France. Although the Republic was never officially proclaimed on 22 September 1792, the decision was made to date the acts from the year I of the Republic. On 25 September 1792, the Republic was declared "one and indivisible". From 1792 to 1802, France was at war with the rest of Europe. It also experienced internal conflicts, including the War in the Vendée, wars in Vendée. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
