Proportjonale

Proportjonale is a term used in mathematics and related disciplines to describe a direct proportional relationship between two quantities. The term is used in several languages, including Norwegian and Danish, to denote that one quantity changes in constant ratio to another. In mathematics, two quantities x and y are in direct proportion if there exists a nonzero constant k such that y = kx. The constant k is called the constant of proportionality and determines the rate at which y changes with x. Proportional relationships are linear through the origin; their graphs are straight lines passing through (0,0) with slope k. If no such constant exists, the relation is not proportional.

There is also inverse proportionality, where y ∝ 1/x and y = k/x, in which y decreases as x increases.

Common examples include distance and time at constant speed (d = vt), and mass proportional to volume for a body with fixed density (m = ρV). Proportjonale relationships are fundamental in scaling, unit conversions, and model-building, because a proportional change in one quantity produces a predictable change in the other.

In engineering and control theory, proportional control uses an output that is proportional to the measurement error, described by u(t) = Kp · e(t). This P-action forms the basis for more complex controllers such as PID systems.

See also: proportion, proportionality, direct proportion, inverse proportion, linear relationship.