Search results
Results from the WOW.Com Content Network
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.
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.
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 .
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. 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 ...
Wasserstein metrics measure the distance between two measures on the same metric space. The Wasserstein distance between two measures is, roughly speaking, the cost of transporting one to the other. The set of all m by n matrices over some field is a metric space with respect to the rank distance (,) = ().
This example shows how Euclidean distance will calculate the distance between objects to determine how similar the items are. Note that most text embeddings will be at least a few hundred dimensions instead of just two. Euclidean distance is a standard distance metric used to measure the dissimilarity between two points in a multi-dimensional ...
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:
A measure for the dissimilarity of two shapes is given by Hausdorff distance up to isometry, denoted D H. Namely, let X and Y be two compact figures in a metric space M (usually a Euclidean space ); then D H ( X , Y ) is the infimum of d H ( I ( X ), Y ) among all isometries I of the metric space M to itself.