|
Francis Buekenhout
Francis Buekenhout (born 23 April 1937 in Ixelles near Brussels) is a Belgian mathematician who introduced Buekenhout geometries and the concept of quadratic sets. Career Buekenhout studied at the University of Brussels under Jacques Tits and Paul Libois. Together with his teacher Jacques Tits, he developed concepts with the diagram geometries, also called Buekenhout geometries or Buekenhout–Tits geometries. These largely disregard the concrete axiom systems of a projective or affine geometry and put these and many other incidence geometries into a common framework. He worked at the ULB from 1960 to 1969 as an assistant to Libois. He was then appointed as extraordinary professor 1969 to 1998, and as ordinary professor from 1977 until his retirement in 2002. He has been a member of the Académie Royale des Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ixelles
( French, ) or (Dutch, ), is one of the 19 municipalities of the Brussels-Capital Region, Belgium. Located to the south-east of Brussels' city centre, it is geographically bisected by the City of Brussels. It is also bordered by the municipalities of Auderghem, Etterbeek, Forest, Uccle, Saint-Gilles and Watermael-Boitsfort. , the municipality had a population of 87,632 inhabitants. The total area is , which gives a population density of . In common with all of Brussels' municipalities, it is legally bilingual (French–Dutch). It is generally considered an affluent area of the city and is particularly noted for its communities of European and Congolese immigrants. Geography Ixelles is located in the south-east of Brussels and is divided into two parts by the Avenue Louise/Louizalaan, which is part of the City of Brussels. The municipality's smaller western part includes the Rue du Bailli/Baljuwstraat and extends roughly from the Avenue Louise to the /, whilst its la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brussels
Brussels (french: Bruxelles or ; nl, Brussel ), officially the Brussels-Capital Region (All text and all but one graphic show the English name as Brussels-Capital Region.) (french: link=no, Région de Bruxelles-Capitale; nl, link=no, Brussels Hoofdstedelijk Gewest), is a region of Belgium comprising 19 municipalities, including the City of Brussels, which is the capital of Belgium. The Brussels-Capital Region is located in the central portion of the country and is a part of both the French Community of Belgium and the Flemish Community, but is separate from the Flemish Region (within which it forms an enclave) and the Walloon Region. Brussels is the most densely populated region in Belgium, and although it has the highest GDP per capita, it has the lowest available income per household. The Brussels Region covers , a relatively small area compared to the two other regions, and has a population of over 1.2 million. The five times larger metropolitan area of Brusse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buekenhout Geometry
In mathematics, a Buekenhout geometry or diagram geometry is a generalization of projective spaces, Tits buildings, and several other geometric structures, introduced by . Definition A Buekenhout geometry consists of a set ''X'' whose elements are called "varieties", with a symmetric reflexive relation on ''X'' called "incidence", together with a function τ called the "type map" from ''X'' to a set Δ whose elements are called "types" and whose size is called the "rank". Two distinct varieties of the same type cannot be incident. A flag is a subset of ''X'' such that any two elements of the flag are incident. The Buekenhout geometry has to satisfy the following axiom: *Every flag is contained in a flag with exactly one variety of each type. Example: ''X'' is the linear subspaces of a projective space with two subspaces incident if one is contained in the other, Δ is the set of possible dimensions of linear subspaces, and the type map takes a linear subspace to its dimension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Set
In mathematics, a quadratic set is a set of points in a projective space that bears the same essential incidence properties as a quadric (conic section in a projective plane, sphere or cone or hyperboloid in a projective space). Definition of a quadratic set Let \mathfrak P=(,,\in) be a projective space. A quadratic set is a non-empty subset of for which the following two conditions hold: :(QS1) Every line g of intersects in at most two points or is contained in . ::(g is called exterior to if , g\cap , =0, tangent to if either , g\cap , =1 or g\cap =g, and secant to if , g\cap , =2.) :(QS2) For any point P\in the union _P of all tangent lines through P is a hyperplane or the entire space . A quadratic set is called non-degenerate if for every point P\in , the set _P is a hyperplane. A Pappian projective space is a projective space in which Pappus's hexagon theorem holds. The following result, due to Francis Buekenhout, is an astonishing statement for finite projective ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free University Of Brussels (1834–1969)
The Free University of Brussels (french: Université libre de Bruxelles, or ULB; nl, Vrije Hogeschool te Brussel, later ''Vrije Universiteit Brussel'') was a university in Brussels, Belgium. Founded in 1834 on the principle of "free inquiry" (''libre examen''), its founders envisaged the institution as a free-thinker reaction to the traditional dominance of Catholicism in Belgian education. The institution was avowedly secular and particularly associated with Liberal political movements during the era of pillarisation. The Free University was one of Belgium's major universities, together with the Catholic University of Leuven and the state universities of Liège and Ghent. The "Linguistic Wars" affected the Free University, which split along language lines in 1969 in the aftermath of student unrest at Leuven the previous year. Today two institutions carry the "Free University of Brussels" name: the French-speaking Université libre de Bruxelles (ULB) and the Dutch-speaking Vr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques Tits
Jacques Tits () (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric. Life and career Tits was born in Uccle to Léon Tits, a professor, and Lousia André. Jacques attended the Athénée of Uccle and the Free University of Brussels. His thesis advisor was Paul Libois, and Tits graduated with his doctorate in 1950 with the dissertation ''Généralisation des groupes projectifs basés sur la notion de transitivité''. His academic career includes professorships at the Free University of Brussels (now split into the Université Libre de Bruxelles and the Vrije Universiteit Brussel) (1962–1964), the University of Bonn (1964–1974) and the Collège de France in Paris, until becoming emeritus in 2000. He changed his citizenship to French in 1974 in order to teach at the Collège de France, which at that point required ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the fol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affine Space
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. In an affine space, there is no distinguished point that serves as an origin. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point. In an affine space, there are instead ''displacement vectors'', also called ''translation'' vectors or simply ''translations'', between two points of the space. Thus it makes sense to subtract two points of the space, giving a translation vector, but it does not make sense to add two points of the space. Likewise, it makes sense to add a displacement vector to a point of an affine space, resulting in a new point translated from the starting point by that vector. Any vector space may be viewed as an affine spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incidence Geometry
In mathematics, incidence geometry is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles, continuity, betweenness, and incidence. An ''incidence structure'' is what is obtained when all other concepts are removed and all that remains is the data about which points lie on which lines. Even with this severe limitation, theorems can be proved and interesting facts emerge concerning this structure. Such fundamental results remain valid when additional concepts are added to form a richer geometry. It sometimes happens that authors blur the distinction between a study and the objects of that study, so it is not surprising to find that some authors refer to incidence structures as incidence geometries. Incidence structures arise naturally and have been studied in various areas of mathematics. Consequently, there are different terminologies to describe these objects. In graph theory they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Académie Royale Des Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the forefront of scientific developments in Europe in the 17th and 18th centuries, and is one of the earliest Academies of Sciences. Currently headed by Patrick Flandrin (President of the Academy), it is one of the five Academies of the Institut de France. History The Academy of Sciences traces its origin to Colbert's plan to create a general academy. He chose a small group of scholars who met on 22 December 1666 in the King's library, near the present-day Bibliothèque Nationals, and thereafter held twice-weekly working meetings there in the two rooms assigned to the group. The first 30 years of the Academy's existence were relatively informal, since no statutes had as yet been laid down for the institution. In contrast to its British ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francois Deruyts Prize
The Francois Deruyts Prize, or Prix Francois Deruyts, is awarded every four years to recognize progress in synthetic or analytic superior geometry. It was established in 1902 by the Académie Royale de Belgique, Classe des Sciences, and carries a monetary award. Originally recipients had to be Belgian, but currently EU nationals are eligible. Recipients The recipients of the Francois Deruyts Prize are:{{Cite web, url=http://www.academieroyale.be/fr/les-concours-prix-subventions-laureats-beneficiaires-classe-sciences/, title=Classe des Sciences, website=www.academieroyale.be, language=fr, access-date=2018-05-09 * 1906: Modeste Stuyvaert * 1910: Joseph Fairon * 1914: Lucien Godeaux * 1918: No award * 1926: No award * 1930: Roland Deaux * 1934: Augustin Delgleize * 1938: Pol Burniat * 1938: Octave Rozet * 1942: Pierre Defrise * 1946: François Jongmans * 1946: Louis Nollet * 1950: Léon-Élie Derwidué * 1954: Guy Hirsch * 1958: Fernand Backes * 1962: Paul Dedecker * 1962: Jacque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belgian Mathematicians
Belgian may refer to: * Something of, or related to, Belgium * Belgians, people from Belgium or of Belgian descent * Languages of Belgium, languages spoken in Belgium, such as Dutch, French, and German * Ancient Belgian language, an extinct language formerly spoken in Gallia Belgica * Belgian Dutch or Flemish, a variant of Dutch *Belgian French, a variant of French * Belgian horse (other), various breeds of horse * Belgian waffle, in culinary contexts * SS ''Belgian'', a cargo ship in service with F Leyland & Co Ltd from 1919 to 1934 *''The Belgian ''The Belgian'' is a 1917 American silent film directed by Sidney Olcott and produced by Sidney Olcott Players with Valentine Grant and Walker Whiteside in the leading roles. It is not known whether the film currently survives. Plot As descr ...'', a 1917 American silent film See also * * Belgica (other) * Belgic (other) {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
