About: Radon's theorem

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In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect. A point in the intersection of these convex hulls is called a Radon point of the set.

Attributes	Values
rdf:type	yago:WikicatLemmas yago:WikicatMathematicalTheorems yago:WikicatTheoremsInConvexGeometry yago:WikicatTheoremsInDiscreteGeometry yago:WikicatTheoremsInGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Lemma106751833 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Radonovo lemma (cs) Satz von Radon (de) Lema de Radon (es) Théorème de Radon (géométrie) (fr) 라돈의 정리 (ko) Radon's theorem (en) Теорема Радона (ru) Теорема Радона (uk)
rdfs:comment	Radonovo lemma je tvrzení v kombinatorické geometrii, které říká, že dostatečně velkou množinu bodů v prostoru lze rozdělit na dvě části tak, aby se jejich konvexní obaly protínaly. Lemma se používá například v důkazu Hellyho věty a je elementárním výsledkem kombinatorické geometrie. (cs) Der Satz von Radon (auch als Lemma von Radon bezeichnet) ist ein Lehrsatz der Konvexgeometrie, welcher auf den österreichischen Mathematiker Johann Radon zurückgeht. Der Satz steht in unmittelbarem Zusammenhang mit dem Satz von Helly und ist über diesen mit anderen klassischen Sätzen der Konvexgeometrie verknüpft. (de) El lema de Radon, o simplemente teorema de Radon es un teorema de . Se enuncia de la siguiente manera: (es) Le théorème de Radon, ou lemme de Radon, sur les ensembles convexes affirme que tout ensemble contenant éléments de admet une partition en deux parties dont les enveloppes convexes et se rencontrent. (fr) 기하학에서, 1921년에 요한 라돈에 의해 출판된 볼록 집합의 라돈의 정리는 어떤 Rd의 점 d + 2 개의 집합이든지 볼록 폐포가 교차하는 두 서로소 집합으로 분할할 수 있다고 한다. 이 볼록 폐포의 교집합에 있는 점을 집합의 라돈 점이라고 부른다. 예를 들어, d = 2인 경우, 유클리드 평면에 있는 어떤 네 점의 집합은 두 방법 중 하나로 나뉘어 질 수 있다. 이것은 세 개의 집합 (삼각형)의 볼록 폐포가 하나의 집합을 포함하는 세 개의 집합과 한 개의 집합을 만들 수 있다; 대신에 두 개의 선분이 교차하도록 하는 양 끝점을 이루는 두 쌍의 점을 만들 수 있다. (ko) Теорема Радона — классический результат комбинаторной геометрии и выпуклого анализа. (ru) В геометрії, теорема Радона на опуклих множинах, опублікована у 1921, стверджує, що будь-яку множину з d + 2 точок в Rd можна розбити на дві неперетинні множини, чиї опуклі оболонки перетинаються. Точка, що належить перетину цих опуклих оболонок, називається точка Радона множини. Наприклад, у цьому випадку d = 2, будь-яка множина з чотирьох точок на евклідовій площині розбивна одним з двох способів. Вона може утворити трійку і одинака, де опукла оболонка трійки містить одинака; або ж, вона може утворити дві пари точок, так що ці точки формують кінці відрізків, що перетинаються. (uk) In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect. A point in the intersection of these convex hulls is called a Radon point of the set. (en)
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dcterms:subject	Theorems in convex geometry Theorems in discrete geometry Convex hulls Geometric transversal theory
Wikipage page ID	1406385 (xsd:integer)
Wikipage revision ID	1039440194 (xsd:integer)
Link from a Wikipage to another Wikipage	Facility location Antimatroid Approximation algorithm Archiv der Mathematik Path graph Undirected graph Induced subgraph Line segment Continuous function Convex set Median Tverberg's theorem Theorems in convex geometry Theorems in discrete geometry Gaussian elimination Geometric median Geometry Convex combination Convex hull Shortest path Simplex Clique number Empty set Mathematische Annalen Acta Mathematica Hungarica Topology American Mathematical Society Convex hulls Partition of a set Carathéodory's theorem (convex hull) Geometric transversal theory Centerpoint (geometry) Graduate Texts in Mathematics Journal of Combinatorial Theory Helly's theorem Affine map Johann Radon Borsuk–Ulam theorem Polynomial time Randomized algorithm Real number Hypersphere VC dimension Journal of the London Mathematical Society Euclidean plane Robust statistics Pacific Journal of Mathematics System of linear equations
Link from a Wikipage to an external page	http://www.almaden.ibm.com/u/kclarkson/center/p.pdf http://projecteuclid.org/euclid.pjm/1102970059 http://jlms.oxfordjournals.org/cgi/reprint/s1-41/1/123.pdf
sameAs	Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem Radon's theorem

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