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A set of 20 points in a 10 × 10 grid, with no three points in a line. 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. The problem concerns lines of all slopes, not only those aligned with the
There exist four points such that no three are collinear (points not on a single line). In an affine plane, two lines are called parallel if they are equal or disjoint. Using this definition, Playfair's axiom above can be replaced by: [2] Given a point and a line, there is a unique line which contains the point and is parallel to the line.
Adding four new points, each being added to all the lines of a single parallel class (so all of these lines now intersect), and one new line containing just these four new points produces the projective plane of order three, a (13 4) configuration. Conversely, starting with the projective plane of order three (it is unique) and removing any ...
An arrangement of nine points (related to the Pappus configuration) forming ten 3-point lines.. In discrete geometry, the original orchard-planting problem (or the tree-planting problem) asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane.
Let L = (P, G, I) be an incidence structure, for which the elements of P are called points and the elements of G are called lines. L is a linear space if the following three axioms hold: (L1) two distinct points are incident with exactly one line. (L2) every line is incident to at least two distinct points. (L3) L contains at least two distinct ...
The two circles in the Two points, one line problem where the line through P and Q is not parallel to the given line l, can be constructed with compass and straightedge by: Draw the line m through the given points P and Q. The point G is where the lines l and m intersect; Draw circle C that has PQ as diameter. Draw one of the tangents from G to ...