# Isotropy

Isotropy (from Greek isos equal ἴσος, and Greek τρόπος tropos turn, direction ) refers to the independence of a property of the direction.

In the considered property, there may be some property (eg physical property parameters of biological, social or social characteristic ).

The direction independence of such properties is synonymous with its homogeneous spatial structure.

## Isotropy in physics

Isotropic radiation is usually meant such radiation that is radiated equally in all directions of the three -dimensional space.

In physics, matter is generally not isotropic at the atomic level. Considering as such block, for example an atom can be regarded as isotropic even still, it does already with the neighboring atoms matter if you look in a direction in which, for example, an atomic nucleus is. If these blocks are not arranged regularly, and you look at the environment in a macroscopic distance, so these differences can pick up in the middle, and the matter appears externally isotropic. This case is also referred to as Quasiisotropie. Wherein material having a regular structure (see grid), the properties also on a macroscopic scale length can be anisotropic.

In theoretical physics, the isotropy of space (3-dimensional ) results in three of the ten classical symmetries. According to the Noether theorem follows from each symmetry, the conservation of a physical quantity, for example, follows from the temporal symmetry of the conservation of energy. From the isotropy of space, the angular momentum conservation law can be derived.

If it is at the considered property is an optical, such as reflection or transmission, a distinction is made in the textbooks generally not between isotropy and Quasiisotropie. As a result, optical isotropy is usually set equal to the term of the property can be characterized by a scalar dielectric function. However, this is only true for example, polycrystalline materials, if the crystallites are small compared to the wavelength. Otherwise, polycrystalline materials depolarize generally linearly polarized light even when they are randomly oriented, except the light is additionally also coherent.

## Transverse isotropy in material science

In a fiber -plastic composite or laminate transverse isotropy refers to a UD - layer, ie a layer only in the fiber direction is direction-dependent properties. In the plane perpendicular to the properties, however, are independent of direction.

## Isotropy and homogeneity

When homogeneity in equal volumes of the same number of shares at isotropy the number of shares is equal in all directions.

## Isotropy in mathematics

The concept of isotropy is used in mathematics in different meanings:

- In the synthetic geometry is called a straight isotropic if it is perpendicular to itself, see Präeuklidische level.
- An element of an Bilinearraumes is called isotropic if it satisfies the equation.