Definition:Symmetry Mapping

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Definition

A symmetry mapping (or just symmetry) of a geometric figure is a bijection from the figure to itself which preserves the distance between points.

In other words, it is a self-congruence.


Intuitively and informally, a symmetry is a movement of the figure so that it looks exactly the same after it has been moved.


Examples

Rotations of Square through $90 \degrees$

Let $S$ be a square embedded in the plane centered at the origin $O$.

A rotation of the plane through an angle of $90 \degrees$ either clockwise or anticlockwise is a symmetry mapping of $S$.


Also see

  • Results about symmetry mappings can be found here.


Linguistic Note

The word symmetry comes from Greek συμμετρεῖν (symmetría) meaning measure together.


Sources