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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 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 through the sphere's interior is the chord between ...
Distance from a point to a line. 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 ...
The Mercator projection (/ mərˈkeɪtər /) is a conformal cylindrical map projection first presented by Flemish geographer and mapmaker Gerardus Mercator in 1569. In the 18th century, it became the standard map projection for navigation due to its property of representing rhumb lines as straight lines.
The Euclidean distance is the length of the displacement vector. The displacement in classical physics measures the change in position of an object during an interval of time. While distance is a scalar quantity, or a magnitude, displacement is a vector quantity with both magnitude and direction. In general, the vector measuring the difference ...
Noting that sin ( π 2 − φ) = cos (φ), the haversine formula immediately follows. To derive the law of haversines, one starts with the spherical law of cosines: As mentioned above, this formula is an ill-conditioned way of solving for c when c is small. Instead, we substitute the identity that cos (θ) = 1 − 2 hav (θ), and also ...
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