# Degrees of freedom

In many scientific fields, the **degrees of freedom** of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation.

In mathematics, this notion is formalized as the dimension of a manifold or an algebraic variety. When *degrees of freedom* is used instead of *dimension*, this usually means that the manifold or variety that models the system is only implicitly defined.
See:

- Degrees of freedom (mechanics), number of independent motions that are allowed to the body or, in case of a mechanism made of several bodies, number of possible independent relative motions between the pieces of the mechanism
- Degrees of freedom (physics and chemistry), a term used in explaining dependence on parameters, or the dimensions of a phase space
- Degrees of freedom (statistics), the number of values in the final calculation of a statistic that are free to vary
- Degrees of freedom problem, the problem of controlling motor movement given abundant degrees of freedom

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