Parametrique

Parametrique, often spelled paramétrique in French and known in English as parametric, is a term used to describe methods or objects defined or controlled by parameters. The central idea is that a system’s form, behavior, or distribution is determined by one or more variables that can be varied to produce different outcomes. This concept appears across mathematics, statistics, and design disciplines, providing a flexible framework for describing complex phenomena.

In mathematics, a parametric description expresses coordinates as functions of one or more parameters. For a plane curve, this takes the form x = x(t), y = y(t), where t ranges over an interval. Parametric representations can describe curves that are difficult to capture with explicit functions. Parametric surfaces extend this idea to three dimensions with mappings X(u,v), Y(u,v), Z(u,v). A classic example is the circle, which can be parameterized by x = r cos t and y = r sin t.

In statistics, parametric models specify a family of distributions through a finite set of parameters, such as the normal distribution characterized by its mean μ and standard deviation σ. Inference involves estimating these parameters from data, often under assumptions about the form of the distribution. This contrasts with non-parametric approaches, which do not assume a fixed parameter set.

In design and computer graphics, parametric modeling expresses geometry and behavior through parameters and constraints. Changes to a parameter automatically propagate through the model, enabling rapid exploration of variants. Parametric design and tools like CAD systems and algorithmic modeling platforms are widely used in architecture, product design, and engineering.

See also: parametric equation, parametric surface, parametric model, parametric statistics, non-parametric.