Difference between revisions of "Measure"
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| − | In [[mathematics]], '''measure''' can mean the amount of [[degree]]s in an [[angle]], the [[length]] of a [[line segment]], or a [[function]] that assigns a [[number]] to [[subset]]s of a given [[set]]. | + | In [[mathematics]], '''measure''' can mean the amount of [[degree (geometry) | degree]]s in an [[angle]], the [[length]] of a [[line segment]], or a [[function]] that assigns a [[number]] to [[subset]]s of a given [[set]]. |
== Line Segments == | == Line Segments == | ||
| Line 9: | Line 9: | ||
The measure of <math>\angle ABC</math> is indicated by <math>\mbox{m}\angle ABC</math>. If <math>\angle ABC\cong\angle DEF</math>, then <math>\mbox{m}\angle ABC=\mbox{m}\angle DEF</math>. | The measure of <math>\angle ABC</math> is indicated by <math>\mbox{m}\angle ABC</math>. If <math>\angle ABC\cong\angle DEF</math>, then <math>\mbox{m}\angle ABC=\mbox{m}\angle DEF</math>. | ||
| − | The measure of an angle can expressed in [[degree]]s or in [[radian]]s. | + | The measure of an angle can expressed in [[Degree (geometry) | degree]]s or in [[radian]]s. |
| + | |||
| + | == Circular arcs == | ||
| + | The measure of an [[arc]] of a given [[circle]] is given by the measure of the [[central angle]] [[subtend]]ed by it. | ||
== Sets == | == Sets == | ||
| − | The measure of a set is known as the set's [[cardinality]]. If <math>S=\{ | + | The measure of a set is known as the set's [[cardinality]]. If <math>S=\{-2,\,\pi,\,7\}</math>, then the cardinality of set <math>S</math> is <math>3</math>. |
== See Also == | == See Also == | ||
| + | * [[Measure theory]] | ||
* [[Counting measure]] | * [[Counting measure]] | ||
* [[Euler measure]] | * [[Euler measure]] | ||
Latest revision as of 09:45, 11 July 2007
This article is a stub. Help us out by expanding it.
In mathematics, measure can mean the amount of degrees in an angle, the length of a line segment, or a function that assigns a number to subsets of a given set.
Line Segments
The measure of 
is indicated by 
, without the bar on top. If 
, then 
.
Angles
The measure of 
is indicated by 
. If 
, then 
.
The measure of an angle can expressed in degrees or in radians.
Circular arcs
The measure of an arc of a given circle is given by the measure of the central angle subtended by it.
Sets
The measure of a set is known as the set's cardinality. If 
, then the cardinality of set 
is 
.
