Erdős–Anning theorem (original) (raw)
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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| dbo: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) |
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| dbp:title | Erdos-Anning Theorem (en) |
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| 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) |
| rdfs:label | Erdős–Anning theorem (en) Théorème d'Erdős-Anning (fr) Теорема Эрдёша — Эннинга (ru) Teorema de Erdős–Anning (pt) |
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