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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 Mahalanobis distance is a measure of the distance between a point and a distribution , introduced by P. C. Mahalanobis in 1936. [1] The mathematical details of Mahalanobis distance has appeared in the Journal of The Asiatic Society of Bengal. [2] Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls ...
The Chebyshev distance between two vectors or points x and y, with standard coordinates and , respectively, is. This equals the limit of the L p metrics : hence it is also known as the L ∞ metric. Mathematically, the Chebyshev distance is a metric induced by the supremum norm or uniform norm. It is an example of an injective metric .
The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the Polish mathematician Hermann Minkowski . Comparison of Chebyshev, Euclidean and taxicab distances for the hypotenuse of a 3-4-5 triangle on a ...
Euler's theorem: In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] or equivalently where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who ...
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