Degrees of freedom

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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, the position of a figure in the plane has three degrees of freedom: its orientation and the two coordinates of any fixed point of the figure.

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:

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