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Eugène Ehrhart
Eugène Ehrhart (29 April 1906 – 17 January 2000) was a French mathematician who introduced Ehrhart polynomial In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a highe ...s in the 1960s. Ehrhart received his high school diploma at the age of 22. He was a mathematics teacher in several high schools, and did mathematics research on his own time. He started publishing in mathematics in his 40s, and finished his PhD thesis at the age of 60. Selected publications *. ReferencesA Tribute to Eugène Ehrhart Philippe Clauss, University of Strasbourg. External linksMathematicians who were late learners?-list – MathOverflow {{DEFAULTSORT: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guebwiller
Guebwiller (french: Guebwiller, ; Alsatian language, Alsatian: ''Gàwiller'' ; ) is a Communes of France, commune in the Haut-Rhin Departments of France, department in Grand Est currently in north-eastern France. It was a Subprefectures in France, sub-prefecture of the department until 2015. It is situated northwest of Mulhouse at the foot of the Vosges mountains. The ''Ballon de Guebwiller'', the highest point in the Vosges, lies to the west of the town. In 2018, Guebwiller had a population of 11,022 and its urban unit, urban area had a population of 28,662. History Guebweiler, as Gebweiler, is mentioned as early as 774. It belonged to the religious foundation of Murbach Abbey, Murbach, and in 1759 the abbots chose it for their residence. In 1789, at the outbreak of the French Revolution, the monastic buildings were laid in ruins, and, though the archives were rescued and removed to Colmar, the library perished. Geography Climate Guebwiller has a oceanic climate (Köppen c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strasbourg
Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the European Parliament. Located at the border with Germany in the historic region of Alsace, it is the prefecture of the Bas-Rhin department. In 2019, the city proper had 287,228 inhabitants and both the Eurométropole de Strasbourg (Greater Strasbourg) and the Arrondissement of Strasbourg had 505,272 inhabitants. Strasbourg's metropolitan area had a population of 846,450 in 2018, making it the eighth-largest metro area in France and home to 14% of the Grand Est region's inhabitants. The transnational Eurodistrict Strasbourg-Ortenau had a population of 958,421 inhabitants. Strasbourg is one of the ''de facto'' four main capitals of the European Union (alongside Brussels, Luxembourg and Frankfurt), as it is the seat of several European insti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pacific and Indian Oceans. Its Metropolitan France, metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean. Due to its several coastal territories, France has the largest exclusive economic zone in the world. France borders Belgium, Luxembourg, Germany, Switzerland, Monaco, Italy, Andorra, and Spain in continental Europe, as well as the Kingdom of the Netherlands, Netherlands, Suriname, and Brazil in the Americas via its overseas territories in French Guiana and Saint Martin (island), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Strasbourg
The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers. The French university traces its history to the earlier German-language ''Universität Straßburg'', which was founded in 1538, and was divided in the 1970s into three separate institutions: Louis Pasteur University, Marc Bloch University, and Robert Schuman University. On 1 January 2009, the fusion of these three universities reconstituted a united University of Strasbourg. With as many as 19 Nobel laureates, and two Fields Medal winners, the university is ranked among the best in the League of European Research Universities. History The university emerged from a Lutheran humanist German Gymnasium, founded in 1538 by Johannes Sturm in the Free Imperial City of Strassburg. It was transformed to a university in 1621 (german: Universität Straßburg) and elevated to the ranks of a royal u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrhart Polynomial
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane. These polynomials are named after Eugène Ehrhart who studied them in the 1960s. Definition Informally, if is a polytope, and is the polytope formed by expanding by a factor of in each dimension, then is the number of integer lattice points in . More formally, consider a lattice \mathcal in Euclidean space \R^n and a -dimensional polytope in \R^n with the property that all vertices of the polytope are points of the lattice. (A common example is \mathcal = \Z^n and a polytope for which all vertices have integer coordinates.) For any positive integer , let be the -fold dilation of (the polytope formed by multiplying each vertex coordinate, in a basis for the la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrhart's Volume Conjecture
In the geometry of numbers, Ehrhart's volume conjecture gives an upper bound on the volume of a convex body containing only one lattice point in its interior. It is a kind of converse to Minkowski's theorem, which guarantees that a centrally symmetric convex body ''K'' must contain a lattice point as soon as its volume exceeds 2^n. The conjecture states that a convex body ''K'' containing only one lattice point in its interior as its Center_of_mass, barycenter cannot have volume greater than (n+1)^n/n!: :\operatorname(K) \le \frac. Equality is achieved in this inequality when K=(n+1)\Delta_n is a copy of the standard simplex in Euclidean ''n''-dimensional space, whose sides are scaled up by a factor of n+1. Equivalently, K=(n+1)\Delta_n is congruent to the convex hull of the vectors -\sum_^n \mathbf_i, and (n+1)\mathbf_j - \sum_^n \mathbf_i for all j=1,\ldots,n . Presented in this manner, the origin is the only lattice point interior to the convex body ''K''. The conjecture, f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1906 Births
Events January–February * January 12 – Persian Constitutional Revolution: A nationalistic coalition of merchants, religious leaders and intellectuals in Persia forces the shah Mozaffar ad-Din Shah Qajar to grant a constitution, and establish a national assembly, the Majlis. * January 16–April 7 – The Algeciras Conference convenes, to resolve the First Moroccan Crisis between France and Germany. * January 22 – The strikes a reef off Vancouver Island, Canada, killing over 100 (officially 136) in the ensuing disaster. * January 31 – The Ecuador–Colombia earthquake (8.8 on the Moment magnitude scale), and associated tsunami, cause at least 500 deaths. * February 7 – is launched, sparking a naval race between Britain and Germany. * February 11 ** Pope Pius X publishes the encyclical ''Vehementer Nos'', denouncing the 1905 French law on the Separation of the Churches and the State. ** Two British members of a poll tax collecting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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