Direct proportionality

Two quantities a and b are said to be directly proportional, if the quotient ${\frac {a}{b}}$ is constant. This is written as $a\propto b$.

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Constant of Proportionality

The constant $c={\frac {a}{b}}$ is called constant of proportionality. Therefore, a proportionality can be written as:

$a=c\times b$

Famous Proportionality

• The circumference C of a circle is proportional to its radius r:

$C\propto r$

Here, the constant is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \pi}

• Mass–energy equivalence: The energy E of a body is proportional to its mass m:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E \propto m}

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C \propto 2 \pi} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E \propto c^2} .

Sources

Weisstein, Eric W. "Proportional." From MathWorld--A Wolfram Web Resource.