Degrees of freedom  

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Kunstformen der Natur (1904) by Ernst Haeckel
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Kunstformen der Natur (1904) by Ernst Haeckel

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:

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Unless indicated otherwise, the text in this article is either based on Wikipedia article "Degrees of freedom" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on research by Jahsonic and friends. See Art and Popular Culture's copyright notice.

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