Isotropy
uniformity in all orientations
In physics and geometry, isotropy (from Ancient Greek ἴσος (ísos) 'equal' and τρόπος (trópos) 'turn, way') is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix a- or 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.
Isotropic quadratic form
A quadratic form q is said to be isotropic if there is a non-zero vector v such that q(v) = 0; such a v is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is an isotropic line.
Isotropic coordinates
Isotropic coordinates are coordinates on an isotropic chart for Lorentzian manifolds.
“Isotropy” enters the record as uniformity in all orientations. Crown Archives preserves that source wording while asking what Isotropy, uniformity and orientations can confirm, complicate or overturn.
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