In geometry, a translation "slides" an object by a **a**: *T*_{a}(**p**) = **p** + **a**.

In physics and mathematics, continuous **translational symmetry** is the invariance of a system of equations under any translation. Discrete translational symmetry is invariance under discrete translation.

Analogously an operator *A* on functions is said to be translation invariant with respect to a translation operator if the result after applying *A* doesn't change if the argument function is translated. More precisely it must hold that

Laws of physics are translationally invariant if they do not distinguish different points in space. According to Noether's theorem, translational symmetry of a physical system is equivalent to the momentum conservation law.

Translational symmetry of an object means that a particular translation does not change the object. For a given object, the translations for which this applies form a group, the symmetry group of the object, or, if the object has more kinds of symmetry, a subgroup of the symmetry group

Read more about Translational Symmetry: Geometry

### Other articles related to "translational symmetry, symmetry":

**Translational Symmetry**

2-fold rotational

**symmetry**together with single

**translational symmetry**is one of the Frieze groups ... Together with double

**translational symmetry**the rotation groups are the following wallpaper groups, with axes per primitive cell p2 (2222) 4Ã—2-fold rotation group of a parallelogrammic, rectangular ... any lattice (every lattice is upside-down the same, but that does not apply for this

**symmetry**) it is e.g ...

... In the case of glide reflection

**symmetry**, the

**symmetry**group of an object contains a glide reflection, and hence the group generated by it ... Example pattern with this

**symmetry**group + + +++ +++ +++ + Frieze group nr ... Example pattern with this

**symmetry**group + + + + + + + + + For any

**symmetry**group containing some glide reflection

**symmetry**, the translation vector of any ...

... Phonons are the result of applying

**translational symmetry**to the potential in a SchrÃ¶dinger equation ... Fractal self-similarity can be thought of as a

**symmetry**somewhat comparable to

**translational symmetry**...

**Translational symmetry**is

**symmetry**under displacement or change of position, and self-similarity is

**symmetry**under change of scale ...

... A lattice is the

**symmetry**group of discrete

**translational symmetry**in n directions ... A pattern with this lattice of

**translational symmetry**cannot have more, but may have less

**symmetry**than the lattice itself ... the orbit of a group action under

**translational symmetry**, is a translate of the translation lattice a coset, which need not contain the origin, and therefore need not be a lattice in the previous sense ...

### Famous quotes containing the word symmetry:

“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial *symmetry* of their position and movements.”

—George Gordon Noel Byron (1788–1824)