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{{Short description|a measure of distance in physical space}} |
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{{Use British English|date=March 2018}} |
{{Use British English|date=March 2018}} |
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{{About|a physical measurement}} |
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{{other uses}} |
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{{ |
{{Redirect|Width||Width (disambiguation)}} |
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{{ |
{{Redirect|Breadth|ship measurements|Breadth (nautical)}} |
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{{Infobox physical quantity |
{{Infobox physical quantity |
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| name = Length |
| name = Length |
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| image = Scale kilometres miles.svg |
| image = Scale kilometres miles.svg |
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| caption = The [[Metric system|metric]] length of one [[kilometre]] is equivalent to the [[imperial measurement]] of 0.62137 [[mile]]s. |
| caption = The [[Metric system|metric]] length of one [[kilometre]] is equivalent to the [[imperial measurement]] of 0.62137 [[mile]]s. |
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| unit = [[ |
| unit = [[metre]] (m) |
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| otherunits = see [[unit of length]] |
| otherunits = see [[unit of length]] |
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| symbols = ''l'' |
| symbols = ''l'' |
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| dimension = '''L''' |
| dimension = '''L''' |
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| extensive = yes |
| extensive = yes |
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}} |
}} |
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'''Length''' is a measure of [[distance]]. In the [[International System of Quantities]], length is a [[quantity]] with dimension [[distance]]. In most [[Measurement system|systems of measurement]], the unit of length is a [[Base unit (measurement)|base unit]], from which other units are derived. |
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'''Length''' is commonly understood to mean the most extended [[dimension]] of an object.<ref>[http://wordnetweb.princeton.edu/perl/webwn?s=length Princeton.edu]</ref> |
'''Length''' is a measure of [[distance]]. In the [[International System of Quantities]], length is a [[quantity]] with dimension [[distance]]. In most [[Measurement system|systems of measurement]], the unit of length is a [[Base unit (measurement)|base unit]], from which other units are derived. Length is commonly understood to mean the most extended [[dimension]] of an object.<ref>[http://wordnetweb.princeton.edu/perl/webwn?s=length Princeton.edu]</ref> |
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Types of length include |
Types of length include [[height]], which is vertical length or vertical extent, and [[width]] or [[breadth]], which are the side-to-side length, measuring across the object at right angles to the height. |
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Length is |
Length is the measure of one spatial dimension, whereas [[area]] is a measure of two dimensions (length squared) and [[volume]] is a measure of three dimensions (length cubed). |
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== History == |
== History == |
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Measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. |
Measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. As trade between different places increased, the need for standard units of length increased. And later, as society has become more technologically oriented, much higher accuracy of measurement is required in an increasingly diverse set of fields, from micro-electronics to interplanetary ranging.<ref>History of Length Measurement, [http://www.npl.co.uk/educate-explore/factsheets/history-of-length-measurement/ National Physical Laboratory]</ref> |
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⚫ | Under [[Albert Einstein|Einstein]]'s [[special relativity]], length can no longer be thought of as being constant in all reference frames. Thus a ruler that is one metre long in one frame of reference will not be one metre long in a reference frame that is moving relative to the first frame. This means the length of an object varies depending on the speed of the observer. |
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As trade between different places increased, the need for standard units of length increased. And later, as society has become more technologically oriented, much higher accuracy of measurement is required in an increasingly diverse set of fields, from micro-electronics to interplanetary ranging.<ref>History of Length Measurement, [http://www.npl.co.uk/educate-explore/factsheets/history-of-length-measurement/ National Physical Laboratory]</ref> |
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== Use in mathematics == |
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⚫ | Under [[Albert Einstein]]'s [[special relativity]], length can no longer be thought of as being constant in all reference frames. Thus a ruler that is one |
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=== Euclidean geometry === |
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{{main|Euclidean geometry}} |
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In Euclidean geometry, length is measured along [[straight line]]s unless otherwise specified. [[Pythagorean theorem|Pythagoras's theorem]] relating the length of the sides of a [[right triangle]] is an application in Euclidean geometry. Length may also be measured along other types of curves and is referred to as [[arclength]] or [[pathlength]]. |
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=== Other geometries === |
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{{see|Non-Euclidean geometry}} |
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In other geometries, length may be measured along curved paths, called [[geodesic]]s. The [[Riemannian geometry]] used in [[general relativity]] is an example of such a geometry. |
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=== Measure theory === |
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{{main|Lebesgue measure}} |
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In measure theory, length is most often generalized to general sets of <math>\mathbb{R}^n</math> via the [[Lebesgue measure]]. In the one-dimensional case, the Lebesgue outer measure of a set is defined in terms of the lengths of open intervals. Concretely, the length of an [[Open Interval|open interval]] is first defined as |
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<math>\ell(\{x\in\mathbb R\mid a<x<b\})=b-a.</math> |
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so that the Lebesgue outer measure <math>\mu^*(E)</math> of a general set <math>E</math> may then be defined as<ref>{{Cite web|url=http://zeta.math.utsa.edu/~mqr328/class/real2/L-measure.pdf|title=Lebesgue Measure|last=Le|first=Dung|date=|website=|url-status=live|archive-url=|archive-date=|access-date=}}</ref><math>\mu^*(E)=\inf\left\{\sum_k \ell(I_k):I_k\text{ is a sequence of open intervals such that }E\subseteq\bigcup_k I_k\right\}.</math> |
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== Units == |
== Units == |
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In the physical sciences and engineering, when one speaks of {{em|units of length}}, the word {{em|length}} is synonymous with [[distance]]. There are several [[Units of measurement|units]] that are used to [[Measurement|measure]] length. Historically, [[unit of length|units of length]] may have been derived from the lengths of human body parts, the distance traveled in a number of paces, the distance between landmarks or places on the Earth, or arbitrarily on the length of some common object. |
In the physical sciences and engineering, when one speaks of {{em|[[unit of length|units of length]]}}, the word {{em|length}} is synonymous with [[distance]]. There are several [[Units of measurement|units]] that are used to [[Measurement|measure]] length. Historically, [[unit of length|units of length]] may have been derived from the lengths of human body parts, the distance traveled in a number of paces, the distance between landmarks or places on the Earth, or arbitrarily on the length of some common object. |
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In the [[International System of Units]] (SI), the [[SI base unit|basic unit]] of length is the [[metre]] and is now defined in terms of the [[speed of light]]. The [[centimetre]] and the [[kilometre]], derived from the metre, are also commonly used units. In [[U.S. customary units]], English or [[Imperial system of units]], commonly used units of length are the [[inch]], the [[foot (length)|foot]], the [[yard]], and the [[mile]]. |
In the [[International System of Units]] (SI), the [[SI base unit|basic unit]] of length is the [[metre]] (symbol, m) and is now defined in terms of the [[speed of light]] (about 300 million metres per [[second]]). The [[millimetre]] (mm), [[centimetre]] (cm) and the [[kilometre]] (km), derived from the metre, are also commonly used units. In [[U.S. customary units]], English or [[Imperial system of units]], commonly used units of length are the [[inch]] (in), the [[foot (length)|foot]] (ft), the [[yard]] (yd), and the [[statute mile|mile]] (mi). A unit of length used in [[navigation]] is the [[nautical mile]] (nmi). |
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Units used to denote distances in the vastness of space, as in [[astronomy]], are much longer than those typically used on Earth and include the [[astronomical unit]], the [[light-year]], and the [[parsec]]. |
Units used to denote distances in the vastness of space, as in [[astronomy]], are much longer than those typically used on Earth and include the [[astronomical unit]] (au), the [[light-year]], and the [[parsec]] (pc). |
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== See also == |
== See also == |
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* [[List_of_humorous_units_of_measurement#Length|Humorous units of length]] |
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*[[Arc length]] |
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*[[ |
* [[Metric system]] |
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* [[Orders of magnitude (length)]] |
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*[[Distance]] |
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*[[ |
* [[Reciprocal length]] |
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*[[Reciprocal length]] |
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*[[Smoot]] |
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*[[Width]] |
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== References == |
== References == |
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{{Commons category}} |
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{{Reflist}} |
{{Reflist}} |
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{{SI base quantities}} |
{{SI base quantities}} |
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