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About: No-three-in-line problem     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatConjecturesyago:WikicatMathematicalProblemsyago:Abstraction100002137yago:Attribute100024264yago:Cognition100023271yago:Concept105835747yago:Condition113920835yago:Content105809192yago:Difficulty114408086yago:Hypothesis105888929yago:Idea105833840yago:Problem114410605yago:PsychologicalFeature100023100yago:Speculation105891783yago:State100024720 New Facet based on Instances of this Class

The no-three-in-line problem in discrete geometry asks how many points can be placed in the grid so that no three points lie on the same line. This number is at most , because points in a grid would include a row of three or more points, by the pigeonhole principle. The problem was introduced by Henry Dudeney in 1900. Brass, Moser, and Pach call it "one of the oldest and most extensively studied geometric questions concerning lattice points". Although originating in recreational mathematics, the problem has applications in graph drawing and to the Heilbronn triangle problem.