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  2. No-three-in-line problem - Wikipedia

    en.wikipedia.org/wiki/No-three-in-line_problem

    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 grid. It was introduced by Henry Dudeney in 1900. Brass, Moser, and Pach call it "one of the oldest and most extensively studied ...

  3. Alphanumeric grid - Wikipedia

    en.wikipedia.org/wiki/Alphanumeric_grid

    An alphanumeric grid (also known as atlas grid [1]) is a simple coordinate system on a grid in which each cell is identified by a combination of a letter and a number. [2]An advantage over numeric coordinates such as easting and northing, which use two numbers instead of a number and a letter to refer to a grid cell, is that there can be no confusion over which coordinate refers to which ...

  4. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    In the cylindrical coordinate system, a z-coordinate with the same meaning as in Cartesian coordinates is added to the r and θ polar coordinates giving a triple (r, θ, z). [8] Spherical coordinates take this a step further by converting the pair of cylindrical coordinates ( r , z ) to polar coordinates ( ρ , φ ) giving a triple ( ρ , θ ...

  5. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    These coordinates are the signed distances from the point to n mutually perpendicular fixed hyperplanes. Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a) 2 + (y − b) 2 = r 2 where a and b are the coordinates of the center (a, b) and r is the radius.

  6. Grid classification - Wikipedia

    en.wikipedia.org/wiki/Grid_classification

    In orthogonal mesh the grid lines are perpendicular to intersection. This is shown in Figure 2. b) Non–orthogonal coordinate. Figure 3 shows non-orthogonal grids. The figure shows the grid lines do not intersect at 90-degree angle. In both these cases the domain boundaries coincide with the coordinate lines; therefore all the geometrical ...

  7. Orthogonal coordinates - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_coordinates

    A conformal map acting on a rectangular grid. Note that the orthogonality of the curved grid is retained. While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum ...

  8. Generalized coordinates - Wikipedia

    en.wikipedia.org/wiki/Generalized_coordinates

    It is ideal to use the minimum number of coordinates needed to define the configuration of the entire system, while taking advantage of the constraints on the system. These quantities are known as generalized coordinates in this context, denoted q j (t). It is convenient to collect them into an n-tuple

  9. Snake Projection - Wikipedia

    en.wikipedia.org/wiki/Snake_Projection

    The Snake Projection is the engineering coordinate system used for a significant proportion of primary rail routes in the UK, [8] including that of the HS2 London to Birmingham high speed line. [9] For the London to Glasgow West Coast Main Line the distortion in the Snake Projection used is no greater than 20 parts per million within 5 ...

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