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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.
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 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 distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line. This distance can be found by first solving the linear systems. and. to get the coordinates of the intersection points. The solutions to the linear systems are the points.
The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after Soviet mathematician Vladimir Levenshtein, who defined the metric in 1965. [1] Levenshtein distance may also be referred to as edit distance, although ...
Angular distance. Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere. When the rays are lines of sight from an observer to two points in space, it is known as the ...
The Hausdorff distance is the longest distance someone can be forced to travel by an adversary who chooses a point in one of the two sets, from where they then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set.
A string metric provides a number indicating an algorithm-specific indication of distance. The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). [ 2] It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order ...