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Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ''an'', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ==Mathematics== Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. A manifold can be homogeneous without being isotropic, but if it is inhomogeneous, it is necessarily anisotropic. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that . ; Isotropic coordinates on an isotropic chart for Lorentzian manifolds. ; Isotropy group: An isotropy group is the group of isomorphisms from any object to itself in a groupoid.〔A groupoid is a category where all morphisms are isomorphisms, i.e., invertible. If is any object, then denotes its isotropy group: the group of isomorphisms from to .〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「isotropy」の詳細全文を読む スポンサード リンク
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