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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 ...
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: ... File talk:No-three-in-line.svg; Global file usage.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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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 ...
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The 9 points and 12 lines of , and a 4-element cap set (the four yellow points) in this space. In affine geometry, a cap set is a subset of the affine space (the -dimensional affine space over the three-element field) where no three elements sum to the zero vector.