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Direct proportionality (view source)
Revision as of 07:41, January 27, 2013
, 07:41, January 27, 2013Used "Direct proportionality" instead of "direct proportional" as proposed
Two quantities '''a''' and '''b''' are said to be '''directly proportional''', if the quotient <math>\frac{a}{b}</math> is constant. This is written as <math>a \propto b</math>.
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== Constant of Proportionality ==
The constant <math>c = \frac{a}{b}</math> is called ''constant of proportionality''. Therefore a ''proportionality'' can be written as:
::::<math>a = c \times b</math>
== Famous Proportionality ==
*The [[circumference]] '''C''' of a [[circle]] is proportional to its [[radius]] '''r''':
:::<math>C \propto r</math>
:Here, the constant is <math>2 \pi</math>
*[[E=mc²|Mass–energy equivalence]]: The [[energy]] '''E''' of a body is proportional to its [[mass]] '''m''':
:::<math>E \propto m</math>
:Here, the constant is '''c²''', the square of the speed of light.
== Misunderstandings ==
The role of the quantities and of the constant are not interchangeable. It would be wrong to say in the examples above that <math>C \propto 2 \pi</math> or <math>E \propto c^2</math>.
== Sources ==
[http://mathworld.wolfram.com/Proportional.html Weisstein, Eric W. "Proportional." From MathWorld--A Wolfram Web Resource.]
[[Category:Mathematics]]
----
== Constant of Proportionality ==
The constant <math>c = \frac{a}{b}</math> is called ''constant of proportionality''. Therefore a ''proportionality'' can be written as:
::::<math>a = c \times b</math>
== Famous Proportionality ==
*The [[circumference]] '''C''' of a [[circle]] is proportional to its [[radius]] '''r''':
:::<math>C \propto r</math>
:Here, the constant is <math>2 \pi</math>
*[[E=mc²|Mass–energy equivalence]]: The [[energy]] '''E''' of a body is proportional to its [[mass]] '''m''':
:::<math>E \propto m</math>
:Here, the constant is '''c²''', the square of the speed of light.
== Misunderstandings ==
The role of the quantities and of the constant are not interchangeable. It would be wrong to say in the examples above that <math>C \propto 2 \pi</math> or <math>E \propto c^2</math>.
== Sources ==
[http://mathworld.wolfram.com/Proportional.html Weisstein, Eric W. "Proportional." From MathWorld--A Wolfram Web Resource.]
[[Category:Mathematics]]