About: Heilbronn triangle problem

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In discrete geometry and discrepancy theory, the Heilbronn triangle problem is a problem of placing points within a region in the plane, in order to avoid triangles of small area. It is named after Hans Heilbronn, who conjectured that, no matter how these points are placed, some triangle will have an area that is at most inversely proportional to the square of the number of points. His conjecture was proven false, but the asymptotic growth rate of the minimum triangle area remains unknown.

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rdf:type	disease
rdfs:label	Heilbronn triangle problem (en)
rdfs:comment	In discrete geometry and discrepancy theory, the Heilbronn triangle problem is a problem of placing points within a region in the plane, in order to avoid triangles of small area. It is named after Hans Heilbronn, who conjectured that, no matter how these points are placed, some triangle will have an area that is at most inversely proportional to the square of the number of points. His conjecture was proven false, but the asymptotic growth rate of the minimum triangle area remains unknown. (en)
sameAs	Heilbronn triangle problem Heilbronn triangle problem
dbp:wikiPageUsesTemplate	dbt:Efn dbt:Harvtxt dbt:Mathworld dbt:Notelist dbt:R dbt:Reflist dbt:Short_description dbt:Unsolved
Subject	Area Discrepancy theory Discrete geometry Triangle problems
thumbnail	wiki-commons:Special:FilePath/6.svg?width=300
foaf:depiction
gold:hypernym	Problem
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Heilbronn_triangle_problem?oldid=1074034812&ns=0
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Wikipage revision ID	1074034812 (xsd:integer)
Link from a Wikipage to another Wikipage	No-three-in-line problem Normalization (statistics) Probabilistic method Proportionality (mathematics) Unit disk Unit square Affine transformation Area Asymptotic analysis Big O notation Binomial distribution Area Discrepancy theory Discrete geometry Girth (graph theory) Discrepancy theory Discrete geometry Pick's theorem Digon Hypercube Hypergraph Prime number Square (algebra) Time complexity Collinearity Compact space Conjecture Convex hull Convex set Hexagon Danzer set Graph removal lemma Expected value Hans Heilbronn Integer lattice Triangle Klaus Roth Kolmogorov complexity Paul Erdős Point-set triangulation Randomized algorithm Range searching Regular polygon Simplex Triangle problems
has abstract	In discrete geometry and discrepancy theory, the Heilbronn triangle problem is a problem of placing points within a region in the plane, in order to avoid triangles of small area. It is named after Hans Heilbronn, who conjectured that, no matter how these points are placed, some triangle will have an area that is at most inversely proportional to the square of the number of points. His conjecture was proven false, but the asymptotic growth rate of the minimum triangle area remains unknown. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Heilbronn_triangle_problem
is Link from a Wikipage to another Wikipage of	List of triangle topics List of unsolved problems in mathematics No-three-in-line problem Discrepancy theory János Komlós (mathematician) János Pintz Danzer set Incompressibility method Index of combinatorics articles Hans Heilbronn Heilbronn (disambiguation) Klaus Roth
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Heilbronn_triangle_problem

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