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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: ... File talk:No-three-in-line.svg; Global file usage.
Animation of the missing square puzzle, showing the two arrangements of the pieces and the "missing" square Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid.
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.
Example of a regular grid. A regular grid is a tessellation of n-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). [1] Its opposite is irregular grid.. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization of parameter spaces.
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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Thus a single line can be drawn connecting all nine dots—which would appear as three lines in parallel on the paper, when flattened out. [18] It is also possible to fold the paper flat, or to cut the paper into pieces and rearrange it, in such a way that the nine dots lie on a single line in the plane (see fold-and-cut theorem). [17]