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  2. Pappus configuration - Wikipedia

    en.wikipedia.org/wiki/Pappus_configuration

    The Pappus configuration, augmented with an additional line (the vertical one in the center of the figure), solves the orchard-planting problem.. A variant of the Pappus configuration provides a solution to the orchard-planting problem, the problem of finding sets of points that have the largest possible number of lines through three points.

  3. Projective plane - Wikipedia

    en.wikipedia.org/wiki/Projective_plane

    Graph of the projective plane of order 7, having 57 points, 57 lines, 8 points on each line and 8 lines passing through each point, where each point is denoted by a rounded rectangle and each line by a combination of letter and number. Only lines with letter A and H are drawn. In the Dobble or Spot It! game, two points are removed.

  4. Intersection (geometry) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(geometry)

    Determination of the intersection of flats – linear geometric objects embedded in a higher-dimensional space – is a simple task of linear algebra, namely the solution of a system of linear equations. In general the determination of an intersection leads to non-linear equations, which can be solved numerically, for example using Newton ...

  5. Configuration (geometry) - Wikipedia

    en.wikipedia.org/wiki/Configuration_(geometry)

    Configurations (4 3 6 2) (a complete quadrangle, at left) and (6 2 4 3) (a complete quadrilateral, at right).. In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.

  6. Orchard-planting problem - Wikipedia

    en.wikipedia.org/wiki/Orchard-planting_problem

    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.

  7. Descriptive geometry - Wikipedia

    en.wikipedia.org/wiki/Descriptive_geometry

    General solutions are a class of solutions within descriptive geometry that contain all possible solutions to a problem. The general solution is represented by a single, three-dimensional object, usually a cone, the directions of the elements of which are the desired direction of viewing (projection) for any of an infinite number of solution views.