proportionell

Proportionell is an adjective meaning proportional or proportionate. In mathematics and related fields, a relationship is called proportional when one quantity is a constant multiple of another. If y is proportional to x, then y = kx for some constant k, and the ratio y/x = k remains constant for all x in the domain. Direct proportionality is contrasted with inverse proportionality, where y ∝ 1/x.

In mathematics, proportional relationships appear in linear functions, direct variation, and scaling phenomena. In physics, many laws reflect proportionality: for example, Hooke’s law F ∝ x for small deformations, and, for a fixed mass, acceleration a ∝ F, so acceleration is proportional to force.

In engineering and control theory, a proportional controller outputs a signal proportional to the error signal. The proportional gain determines response speed and stability; simple P controllers are often used alone or as part of PID control, which also includes integral and derivative terms to improve performance.

In other domains, proportional concepts appear in statistics and politics, such as proportional representation, where seats or resources are allocated in proportion to shares of votes or resources.

Limitations of proportionality arise in real systems due to nonlinearities, saturation, thresholds, and changing conditions; beyond a certain range, the relationship may no longer be proportional. Understanding when proportionality holds helps model, predict, and control many natural and engineered processes.