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The denominator of this expression is the distance between P 1 and P 2. The numerator is twice the area of the triangle with its vertices at the three points, (x 0,y 0), P 1 and P 2. See: Area of a triangle § Using coordinates.
That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is the start and which is the destination. [11] It is positive, meaning that the distance between every two distinct points is a positive number, while the distance from any point to itself is zero. [11]
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation , it is a special case of a more general formula in spherical trigonometry , the law of haversines , that relates the sides and angles of spherical triangles.
A tunnel between points on Earth is defined by a Cartesian line through three-dimensional space between the points of interest. The tunnel distance D t = 2 R sin D 2 R {\displaystyle D_{\textrm {t}}=2R\sin {\frac {D}{2R}}} is the great-circle chord length and may be calculated as follows for the corresponding unit sphere:
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
In the maximum metric, the distance between two points is the maximum of the absolute values of differences of their x- and y-coordinates. The last two metrics appear, for example, in routing a machine that drills a given set of holes in a printed circuit board. The Manhattan metric corresponds to a machine that adjusts first one coordinate ...
the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
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