View source for Direct proportionality

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. &quot;Proportional.&quot; From MathWorld--A Wolfram Web Resource.]

[[Category:Mathematics]]