About: Erdős–Anning theorem

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The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erdős and Norman H. Anning, who published a proof of it in 1945.

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rdfs:label	Erdős–Anning theorem (en) Théorème d'Erdős-Anning (fr) Теорема Эрдёша — Эннинга (ru) Teorema de Erdős–Anning (pt)
rdfs:comment	The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erdős and Norman H. Anning, who published a proof of it in 1945. (en) En géométrie discrète, le théorème d'Erdős-Anning établit que si une infinité de points d'un espace euclidien sont tous à des distances entières les uns des autres, alors ils sont alignés. (fr) Теорема Эрдёша — Эннинга — утверждение о том, что бесконечное множество точек на плоскости может иметь целые расстояния между точками множества только в том случае, когда все точки лежат на одной прямой. Названа по именам Пала Эрдёша и (англ. Norman Herbert Anning), опубликовавших её доказательство в 1945 году. (ru) O Teorema de Erdős–Anning afirma que um conjunto infinito de pontos no plano que têm distâncias mútuas inteiras pode existir se e somente se todos os pontos estão em linha reta. O nome é uma homenagem a Paul Erdős e , que o provaram em 1945. (pt)
dcterms:subject	Articles containing proofs Theorems in discrete geometry Arithmetic problems of plane geometry Theorems in discrete mathematics Paul Erdős
Wikipage page ID	12600251 (xsd:integer)
Wikipage revision ID	1020373851 (xsd:integer)
Link from a Wikipage to another Wikipage	Paul Erdős Infinite set Articles containing proofs Theorems in discrete geometry Arithmetic problems of plane geometry Erdős–Diophantine graph Erdős–Ulam problem Similarity (geometry) Dense set Straight line Triangle inequality Theorems in discrete mathematics Norman H. Anning Hyperbola Paul Erdős Integer Rational number Least common denominator
sameAs	Erdős–Anning theorem Erdős–Anning theorem Erdős–Anning theorem Erdős–Anning theorem Erdős–Anning theorem Erdős–Anning theorem Erdős–Anning theorem
dbp:wikiPageUsesTemplate	dbt:Main dbt:Mathworld dbt:Reflist dbt:Short_description
title	Erdos-Anning Theorem (en)
urlname	Erdos-AnningTheorem (en)
has abstract	The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erdős and Norman H. Anning, who published a proof of it in 1945. (en) En géométrie discrète, le théorème d'Erdős-Anning établit que si une infinité de points d'un espace euclidien sont tous à des distances entières les uns des autres, alors ils sont alignés. (fr) Теорема Эрдёша — Эннинга — утверждение о том, что бесконечное множество точек на плоскости может иметь целые расстояния между точками множества только в том случае, когда все точки лежат на одной прямой. Названа по именам Пала Эрдёша и (англ. Norman Herbert Anning), опубликовавших её доказательство в 1945 году. (ru) O Teorema de Erdős–Anning afirma que um conjunto infinito de pontos no plano que têm distâncias mútuas inteiras pode existir se e somente se todos os pontos estão em linha reta. O nome é uma homenagem a Paul Erdős e , que o provaram em 1945. Uma maneira alternativa de enunciar o teorema é que um conjunto de pontos não colineares no plano com distâncias inteiras pode apenas ser ampliado adicionando-se um número finito de pontos adicionais, antes que não se possa adicionar mais pontos. Mais especificamente, se um conjunto de três ou mais pontos não colineares tem distâncias inteiras, nenhuma excedendo algum número d, então no máximo pontos a distâncias inteiras podem ser adicionados ao conjunto. (pt)
prov:wasDerivedFrom	wikipedia-en:Erdős–Anning_theorem?oldid=1020373851&ns=0
page length (characters) of wiki page	4373 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Erdős–Anning_theorem
is Link from a Wikipage to another Wikipage of	List of scientific laws named after people Erdős–Diophantine graph Erdős–Ulam problem Combinatorial Geometry in the Plane Distance set Norman H. Anning Harborth's conjecture Erdos–Anning theorem Erdős-Anning theorem József Solymosi List of theorems List of things named after Paul Erdős Erdos-Anning theorem
is Wikipage redirect of	Erdos–Anning theorem Erdős-Anning theorem Erdos-Anning theorem
is foaf:primaryTopic of	wikipedia-en:Erdős–Anning_theorem

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