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The no-three-in-line drawing of a complete graph is a special case of this result with =. [12] The no-three-in-line problem also has applications to another problem in discrete geometry, the Heilbronn triangle problem. In this problem, one must place points, anywhere in a unit square, not restricted to a grid. The goal of the placement is to ...
Solutions to the no-three-in-line problem, large sets of grid points with no three collinear points, can be scaled into a unit square with minimum triangle area (/). In the other direction, Paul Erdős found examples of point sets with minimum triangle area proportional to 1 / n 2 {\displaystyle 1/n^{2}} , demonstrating that, if true, Heilbronn ...
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3 Did you know nomination. 4 comments. 4 Defining the grid size. 2 comments. ... Talk: No-three-in-line problem. Add languages. Page contents not supported in other ...
Tools. Tools. move to sidebar hide. Actions Read; View on Commons ... A set of 20 points in a 10 × 10 grid, with no three points in a line. Date: 5 May 2007: Source ...
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The blue points have big lines of up to ten points, but no big clique (the largest mutually-visible subsets of any convex grid subset have only four points). The yellow points form a big clique of ten points, but have no big line (the largest collinear subset of points in convex position has only two points).