Proportionality (mathematics)

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In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. 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 product.

Two functions ${\displaystyle f(x)}$ and ${\displaystyle g(x)}$ are proportional if their ratio ${\textstyle {\frac {f(x)}{g(x)}}}$ is a constant function.

If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., ⁠a/b⁠ = ⁠x/y⁠ = ⋯ = k (for details see Ratio). Proportionality is closely related to linearity.