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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 ...
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.
Great-circle navigation. Great-circle navigation or orthodromic navigation (related to orthodromic course; from Ancient Greek ορθός (orthós) 'right angle' and δρόμος (drómos) 'path') is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such routes yield the shortest distance between two points on the globe.
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.
The shortest distance between two points in plane is a Cartesian straight line. The Pythagorean theorem is used to calculate the distance between points in a plane. Even over short distances, the accuracy of geographic distance calculations which assume a flat Earth depend on the method by which the latitude and longitude coordinates have been ...
For two points, A and B, separated by 10° of longitude on the parallel at 60° the distance along the parallel is approximately 0.5 km greater than the great circle distance. (The distance AB along the parallel is (a cos φ) λ. The length of the chord AB is 2(a cos φ) sin λ / 2 .
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 ...
The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth 's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways.