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Desargues
Girard Desargues (; 21 February 1591September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Biography Born in Lyon, Desargues came from a family devoted to service to the French crown. His father was a royal notary, an investigating commissioner of the Seneschal's court in Lyon (1574), the collector of the tithes on ecclesiastical revenues for the city of Lyon (1583) and for the diocese of Lyon. Girard Desargues worked as an architect from 1645. Prior to that, he had worked as a tutor and may have served as an engineer and technical consultant in the entourage of Richelieu. Yet his involvement in the Siege of La Rochelle, though alleged by Ch. Weiss in ''Biographie Universelle'' (1842), has never been testified. As an architect, Desargues planned several private and public buildings in Paris and Lyon. As an eng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desargues' Theorem
In projective geometry, Desargues's theorem, named after Girard Desargues, states: :Two triangles are in perspective ''axially'' if and only if they are in perspective ''centrally''. Denote the three vertices of one triangle by and , and those of the other by and . ''Axial perspectivity'' means that lines and meet in a point, lines and meet in a second point, and lines and meet in a third point, and that these three points all lie on a common line called the ''axis of perspectivity''. ''Central perspectivity'' means that the three lines and are concurrent, at a point called the ''center of perspectivity''. This intersection theorem is true in the usual Euclidean plane but special care needs to be taken in exceptional cases, as when a pair of sides are parallel, so that their "point of intersection" recedes to infinity. Commonly, to remove these exceptions, mathematicians "complete" the Euclidean plane by adding points at infinity, following Jean-Victor Poncelet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desargues Configuration
In geometry, the Desargues configuration is a Configuration (geometry), configuration of ten points and ten lines, with three points per line and three lines per point. It is named after Girard Desargues. The Desargues configuration can be constructed in two dimensions from the points and lines occurring in Desargues's theorem, in three dimensions from five planes in general position, or in four dimensions from the 5-cell, the four-dimensional regular simplex. It has a large group of symmetries, taking any point to any other point and any line to any other line. It is also self-dual, meaning that if the points are replaced by lines and vice versa using projective duality, the same configuration results. Graph (discrete mathematics), Graphs associated with the Desargues configuration include the Desargues graph (its graph of point-line incidences) and the Petersen graph (its graph of non-incident lines). The Desargues configuration is one of ten different configurations with ten p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desargues Graph
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after Girard Desargues, arises from several different combinatorial constructions, has a high level of symmetry, is the only known non-planar cubic partial cube, and has been applied in chemical databases. The name "Desargues graph" has also been used to refer to a ten-vertex graph, the complement of the Petersen graph, which can also be formed as the bipartite half of the 20-vertex Desargues graph. Constructions There are several different ways of constructing the Desargues graph: *It is the generalized Petersen graph . To form the Desargues graph in this way, connect ten of the vertices into a regular decagon, and connect the other ten vertices into a ten-pointed star that connects pairs of vertices at distance three in a second decagon. The Desargues graph consists of the 20 edges of these two polygons together with an additional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desarguesian Plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus ''any'' two distinct lines in a projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by , RP2, or P2(R), among other notations. There are many other projective planes, both infinite, such as the complex projective plane, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-Desarguesian Plane
In mathematics, a non-Desarguesian plane is a projective plane that does not satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that is not a Desarguesian plane. The theorem of Desargues is true in all projective spaces of dimension not 2; in other words, the only projective spaces of dimension not equal to 2 are the classical projective geometries over a field (or division ring). However, David Hilbert found that some projective planes do not satisfy it. The current state of knowledge of these examples is not complete. Examples There are many examples of both finite and infinite non-Desarguesian planes. Some of the known examples of infinite non-Desarguesian planes include: * The Moulton plane. * Moufang planes over alternative division algebras that are not associative, such as the projective plane over the octonions. Since all finite alternative division rings are fields ( Artin–Zorn theorem), the only non-Desarguesian Moufang planes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''projective space'') and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "Point at infinity, points at infinity") to Euclidean points, and vice versa. Properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translation (geometry), translations (the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. Unlike in Euclidean geometry, the concept of an angle does not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desargues (crater)
Desargues is an ancient Lunar craters, lunar impact crater that is located near the northern limb of the Moon, on the western sphere, hemisphere. It lies nearly due south of the crater Pascal (crater), Pascal, and southeast of Brianchon (crater), Brianchon. The proximity of this crater to the limb means that it appears highly elongated due to foreshortening, and it is difficult to discern details from the Earth. This formation has been significantly eroded and degraded with the passage of time, leaving a low, irregular rim that has been reshaped by subsequent impacts. The rim has a notable bulge to the northeast, and a lesser bulge along the southern rim. The later remains as an imprint of a Palimpsest, ghost crater in the surface that overlies the southern rim, and leaves a remnant of its northern rim in the crater floor. The bulge to the northeast has left a remnant of its origin in the crater floor, as a series of low hills extending from the north and southeast. These enclose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henri Brocard
Pierre René Jean Baptiste Henri Brocard (; 12 May 1845 – 16 January 1922) was a French meteorologist and mathematician, in particular a geometer. His best-known achievement is the invention and discovery of the properties of the Brocard points, the Brocard circle, and the Brocard triangle, all bearing his name. Contemporary mathematician Nathan Court wrote that he, along with Émile Lemoine and Joseph Neuberg, was one of the three co-founders of modern triangle geometry. He was awarded the Ordre des Palmes Académiques, and was an officer of the Légion d'honneur. He spent most of his life studying meteorology as an officer in the French Navy, but seems to have made no notable original contributions to the subject. Biography Early years Pierre René Jean Baptiste Henri Brocard was born on 12 May 1845, in Vignot, Meuse to Elizabeth Auguste Liouville and Jean Sebastien Brocard. He attended the Lycée in Marseille as a young child, and then the Lycée in Strasbour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
René Taton
René Taton (4 April 1915 – 9 August 2004) was a French mathematician, historian of science, and long co-chief-editor of the ''Revue d'histoire des sciences''. He was awarded both the highest lifetime achievement awards in the field of history of science: the George Sarton Medal, in 1975, and the Alexandre Koyré Medal, in 1997. Life Taton was born on 4 April 1915 in L'Échelle, France. In 1935, he became a student of École normale supérieure de Saint-Cloud. He was a mathematician before moving to the history of science, and in 1951 cemented the move by earning a ''doctorat d'état ès lettres'' with philosopher Gaston Bachelard as his advisor, focusing on the history of projective geometry; his primary thesis concerned the work of Gaspard Monge and his accessory thesis concerned Girard Desargues. He died on 9 August 2004 in Ajaccio, Corsica, France. Career Taton was an early participant in Alexandre Koyré's Centre de Recherches en Histoire des Sciences et des Tech ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1591 Births
Events January–March * January 27 – Scottish schoolmaster John Fian becomes the first person to be executed after the North Berwick witch trials, following his conviction for the crime of witchcraft. Fian is taken to the Castlehill outside of Edinburgh and strangled after which his body is burned. Agnes Sampson is garroted the next day at Castlehill and then burned. * February 7 – Pope Gregory XIV, who had succeeded Pope Urban VII in December, appoints Cardinal Marco Antonio Colonna and six other cardinals to a commission to revise the Sixtine Vulgate Latin translation of the Bible, published in 1590 under the editorship of Pope Sixtus V, to which the College of Cardinals has taken exception. The revision of the revision, dubbed the Sixto-Clementine Vulgate, will be completed in 1592 and be the official version used by the Catholic Church until 1979. * February 25 – Poet Edmund Spenser is granted an annual pension of 50 pounds sterling by Que ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeremy Gray
Jeremy John Gray (born 25 April 1947) is an English mathematician primarily interested in the history of mathematics. Biography Gray studied mathematics at the University of Oxford from 1966 to 1969, and then at Warwick University, obtaining his PhD in 1980 under the supervision of Ian Stewart and David Fowler. He has worked at the Open University since 1974, and became a lecturer there in 1978. He also lectured at the University of Warwick from 2002 to 2017, teaching a course on the history of mathematics. Gray was a consultant on the television series, '' The Story of Maths'',''To Infinity and Beyond'' 27 October 2008 21:00 BBC Four a co-production between the Open University and the BBC. He edits Archive for History of Exact Sciences. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. In 2012 he became a fellow of the American Mathematical Society. Books Gray has been awarded prizes for his contributions to mathematics, includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perspective (visual)
Linear or point-projection perspective () is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer increases, and that they are subject to , meaning that an object's dimensions parallel to the line of sight appear shorter than its dimensions perpendicular to the line of sight. All objects will recede to points in the distance, usually along the horizon line, but also above and below the horizon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
