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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 ...
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 ...
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
The topographical surface of the Earth, when each cell of the grid has its surface-position coordinates and the elevation in relation to the standard Geoid. Example: grid with coordinates (φ,λ,z) where z is the elevation. A standard Geoid surface. The z coordinate is zero for all grid, thus can be omitted, (φ,λ).
A common type of lattice graph (known under different names, such as grid graph or square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, x-coordinates being in the range 1, ..., n, y-coordinates being in the range 1, ..., m, and two vertices being connected by an edge whenever the corresponding points are at distance 1.
Another alternative hierarchical grid is the Quadrilateralized Spherical Cube. The 12 "base resolution pixels" of H=4, K=3 HEALPix projection may be thought of as the facets of a rhombic dodecahedron. The H=6 HEALPix has similarities to another alternative grid based on the icosahedron. [12]
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 ...
The two grids covering the Arctic and Antarctic. The universal polar stereographic (UPS) coordinate system is used in conjunction with the universal transverse Mercator (UTM) coordinate system to locate positions on the surface of the Earth. Like the UTM coordinate system, the UPS coordinate system uses a metric-based cartesian grid laid out on ...
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