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The Euclidean distance is the prototypical example of the distance in a metric space, [10] and obeys all the defining properties of a metric space: [11] It is symmetric, meaning that for all points and , (,) = (,). That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is ...
The metric system is a decimal -based system of measurement. The current international standard for the metric system is the International System of Units (Système international d'unités or SI), in which all units can be expressed in terms of seven base units: the metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and ...
Hausdorff distance. In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, [1][2] measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff and Dimitrie ...
The International System of Units, internationally known by the abbreviation SI (from French Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures (abbreviated BIPM from French: Bureau international des ...
The comoving distance from an observer to a distant object (e.g. galaxy) can be computed by the following formula (derived using the Friedmann–Lemaître–Robertson–Walker metric): = ′ (′) where a(t′) is the scale factor, t e is the time of emission of the photons detected by the observer, t is the present time, and c is the speed of ...
Definition. Formally, a metric space is an ordered pair (M, d) where M is a set and d is a metric on M, i.e., a function satisfying the following axioms for all points : [4][5] The distance from a point to itself is zero: (Positivity) The distance between two distinct points is always positive:
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 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.