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Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek ...
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [ 2 ]
Vincenty's formulae. 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 ...
Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path between the two points on the surface of the sphere. (By comparison, the shortest path passing ...
Manhattan distance is commonly used in GPS applications, as it can be used to find the shortest route between two addresses. [ citation needed ] When you generalize the Euclidean distance formula and Manhattan distance formula you are left with the Minkowski distance formulas, which can be used in a wide variety of applications.
Snell underestimated the distance by 3.5%. The two towns were separated by one degree on the meridian, so from his measurement he was able to calculate a value for the circumference of the earth – a feat celebrated in the title of his book Eratosthenes Batavus (The Dutch Eratosthenes), published in 1617. Snell calculated how the planar ...
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