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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 ...
A set of 20 points in a 10 × 10 grid, with no three points in a line. Date: 5 May 2007: Source: Own work: Author: ... should be no visible change to image: 04:27, 6 ...
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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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Note the grid point where the red and blue triangles in the lower image meet (5 squares to the right and two units up from the lower left corner of the combined figure), and compare it to the same point on the other figure; the edge is slightly under the mark in the upper image, but goes through it in the lower.
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