[share]

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.

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

https://en.wikipedia.org/wiki/Degrees_of_freedom