A **one-dimensional symmetry group** is a mathematical group that describes symmetries in one dimension (1D).

A pattern in 1D can be represented as a function *f*(*x*) for, say, the color at position *x*.

The 1D isometries map *x* to *x* + *a* and to *a* − *x*. Isometries which leave the function unchanged are translations *x* + *a* with a such that *f*(*x* + *a*) = *f*(*x*) and reflections *a* − *x* with a such that *f*(*a* − *x*) = *f*(*x*).

Read more about One-dimensional Symmetry Group: Translational Symmetry, Patterns Without Translational Symmetry, 1D-symmetry of A Function Vs. 2D-symmetry of Its Graph, Group Action, Orbits and Stabilizers

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

**One-dimensional Symmetry Group**- Orbits and Stabilizers

... Consider a

**group**G acting on a set X ... The orbit of x is denoted by Gx Case that the

**group**action is on R For the trivial

**group**, all orbits contain only one element for a

**group**of translations, an orbit is e.g ... {2,4}, and for the

**symmetry group**with translations and reflections, e.g ...

### Famous quotes containing the words group and/or symmetry:

“Now, honestly: if a large *group* of ... demonstrators blocked the entrances to St. Patrick’s Cathedral every Sunday for years, making it impossible for worshipers to get inside the church without someone escorting them through screaming crowds, wouldn’t some judge rule that those protesters could keep protesting, but behind police lines and out of the doorways?”

—Anna Quindlen (b. 1953)

“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)