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{{wiktionary|metric|-metric}}
The '''Metric''' System is a common term for the '''[[SI|International System of Units]]'''.
'''Metric''' or '''metrical''' may refer to:
----
In [[mathematics]], a '''metric''' (also called '''distance metric''') on a set is an abstraction of the notion of ''distance''.


{{TOC right}}
Intuitively, the distance between two point is a real, positive number, with the following properties:
==Measuring==
* it is zero only if the two points are in fact the same
* [[Metric system]], an internationally adopted decimal system of measurement
* it does not depend on the order in which points are given (the distance from London to Paris is the same as the distance from Paris to London)
* An adjective indicating relation to [[measurement]] in general, or a noun describing a specific type of measurement
* it satisfies the [[Triangle inequality]]: the distance between two points is never longer than going via a third intermediary point


== Mathematics ==
Formally, let P be a set. A distance metric on P is a function mapping [[ordered pair]]s of elements of P, ( p , q ) to the positive [[Real number]]s:
: ''d'' : '''P''' × '''P''' → '''R+'''


In mathematics, '''metric''' may refer to one of two related, but distinct concepts:
Furhermore, it must satisfy the following three axioms:
* A function which measures distance between two points in a [[metric space]]
* A [[metric tensor]], in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold


== Natural sciences ==
* ''d''( p , q ) = 0 ⇔ p=q (the distance between two points is zero if and only if the two points are the same)
* [[Metric tensor (general relativity)]], the fundamental object of study in general relativity, similar to the gravitational field in Newtonian physics
* ''d''( p , q ) = ''d''( q , p ) for all p,q in P (the distance between p and q is the same and the distance between q and p)
* Senses related to measurement:
* ''d''( p , q ) + ''d''( q , r ) ≥ ''d''( p , r ) for all p,q,r in P (the sum of the distances between p and q and between q and r is greater than or equal to the distance between p and r)
** [[Metric system]], an internationally adopted decimal system of measurement
** [[Metric units]], units related to a metric system
** [[International System of Units]], or ''Système International'' (SI), the most widely used metric system
* [[METRIC]], a model that uses Landsat satellite data to compute and map evapotranspiration (ET) in climatology/meteorology


== Engineering and business ==
Defining a metric on a set allows the notion of open sets limits to be defined on it.
The word '''metric''' is often used to mean a [[descriptive statistic]], [[indicator (statistics)|indicator]], or [[figure of merit]] used to describe or measure something quantitatively, including:
* [[Performance indicator]], a measure of an organization's activities and performance
* [[Metrics (networking)]], the properties of a communication path used by a router to make routing decisions
* [[Software metric]], a measure of some property of a piece of software or its specifications
* [[Reuse metrics]], a quantitative indicator of an attribute for software reuse and reusability
* [[Search engine optimization metrics]], indicators of a website's organic search potential


== Music ==
The metric d gives rise to a [[topology]] on P;
* [[Alex Metric]] (born 1984), British musician, DJ and producer
a basis for this topology is the collection of sets { q: d(p,q)<e} for p in P and e>0.
* [[Metric (band)]], a Canadian rock band founded in Toronto, Ontario


== Other uses ==
In other words, a subset S of P is open in the metric topology if for every point p in S there is a number e>0 such that S contains the set { q: d(p,q)<e}.
* [[Metre (poetry)]], the rhythmic structure of poetry
* [[Typographic measurement|Font metrics]], properties describing the overall shape of a font


See also [[Normed vector space]].
==See also==
* [[Meter (disambiguation)]]
* [[Metrecal]], a diet drink introduced in the 1960s
* [[Metric conversion (disambiguation)]]
* [[Metric dimension (disambiguation)]]
* [[Metric gauge (disambiguation)]]
* {{look from}}

{{disambiguation}}

Latest revision as of 16:46, 6 March 2024

Look up metric or -metric in Wiktionary, the free dictionary.

Metric or metrical may refer to:

Measuring

[edit]
  • Metric system, an internationally adopted decimal system of measurement
  • An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement

Mathematics

[edit]

In mathematics, metric may refer to one of two related, but distinct concepts:

  • A function which measures distance between two points in a metric space
  • A metric tensor, in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold

Natural sciences

[edit]
  • Metric tensor (general relativity), the fundamental object of study in general relativity, similar to the gravitational field in Newtonian physics
  • Senses related to measurement:
  • METRIC, a model that uses Landsat satellite data to compute and map evapotranspiration (ET) in climatology/meteorology

Engineering and business

[edit]

The word metric is often used to mean a descriptive statistic, indicator, or figure of merit used to describe or measure something quantitatively, including:

Music

[edit]
  • Alex Metric (born 1984), British musician, DJ and producer
  • Metric (band), a Canadian rock band founded in Toronto, Ontario

Other uses

[edit]

See also

[edit]
Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Metric&oldid=1212200219"