Proportionality (mathematics)

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, two <a href="/facts/Sequence/gV2S4uqp">sequences</a> of numbers, often <a href="/facts/Experimental_data/PKMa2Fvw">experimental data</a>, are proportional or directly proportional if their corresponding elements have a <a href="/facts/Constant_(mathematics)/SxlxTWFT">constant</a> <a href="/facts/Ratio/mFmhQt7T">ratio</a>. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing constant). Two sequences are inversely proportional if corresponding elements have a constant <a href="/facts/Product_(mathematics)/aXY11nGS">product</a>.
Two <a href="/facts/Function_(mathematics)/CdReEKCh">functions</a> 
 
 
 
 f
 (
 x
 )
 
 
 {\displaystyle f(x)}
 
 and 
 
 
 
 g
 (
 x
 )
 
 
 {\displaystyle g(x)}
 
 are proportional if their ratio 
 
 
 
 
 
 
 f
 (
 x
 )
 
 
 g
 (
 x
 )
 
 
 
 
 
 {\textstyle {\frac {f(x)}{g(x)}}}
 
 is a <a href="/facts/Constant_function/BmPx6dn7">constant function</a>.
If several pairs of variables share the same direct proportionality constant, the <a href="/facts/Equation/pxFzLAVR">equation</a> expressing the equality of these ratios is called a proportion, e.g., ⁠a/b⁠ = ⁠x/y⁠ = ⋯ = k (for details see <a href="/facts/Ratio/mFmhQt7T">Ratio</a>).
Proportionality is closely related to <a href="/facts/Linearity/fChtg3KC">linearity</a>.

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Proportionality (mathematics)