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Concept
Proportionality (mathematics)
Summary
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, also called the coefficient of proportionality.
This definition is commonly extended to related varying quantities, which are often called variables. This meaning of variable is not the common meaning of the term in mathematics (see variable (mathematics)); these two different concepts share the same name for historical reasons.
Two functions and are proportional if their ratio 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.
Equals sign
Given an independent variable x and a dependent variable y, y is directly proportional to x if there is a non-zero constant k such that
The relation is often denoted using the symbols "∝" (not to be confused with the Greek letter alpha) or "~":
or
For the proportionality constant can be expressed as the ratio
It is also called the constant of variation or constant of proportionality.
A direct proportionality can also be viewed as a linear equation in two variables with a y-intercept of 0 and a slope of k. This corresponds to linear growth.
If an object travels at a constant speed, then the distance traveled is directly proportional to the time spent traveling, with the speed being the constant of proportionality.
The circumference of a circle is directly proportional to its diameter, with the constant of proportionality equal to pi.
Official source
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