NonProportional

Nonproportional is an adjective used to describe a relationship in which one quantity is not a constant multiple of another. In mathematics, a proportional relationship has the form y = kx, where k is a constant. When a pair of variables is nonproportional, no single constant k relates them across all values: the ratio y/x varies with x or the relationship is nonlinear.

Common nonproportional relationships include quadratic, cubic, exponential, or logarithmic forms, such as y = ax^2, y = e^x, or y = log x. These functions do not have constant slopes through the origin and do not scale linearly with input.

Nonproportionality is also a standard concern in measurement and instrumentation. Sensor response that deviates from linearity exhibits nonproportionality: the output is not a fixed multiple of the input across the operating range. Calibration or compensation is used to correct for nonproportional behavior and expand the usable dynamic range.

In other domains such as biology, nonproportional scaling (allometry) describes how traits do not increase in direct proportion to overall size, leading to different scaling exponents for different traits. In physics and economics, the term may informally describe systems where effects do not scale linearly with cause or input.

Because nonproportionality implies nonlinearity, it often necessitates more complex models, piecewise fits, or numerical methods to analyze and predict behavior.