Term that refers to a property or a set that is preserved under the effect of a relation.
A set E is generally invariant by a relation ℜ if ℜ(E) = E.
Examples
Invariant set:
- In a reflection, the line of reflection is an invariant line (fixed line) for this transformation.
- In a rotation, the centre of rotation is an invariant point (fixed point) for this transformation.
- A circle is generally invariant by a point symmetry in which the centre of symmetry is the centre of the circle.
Invariant property:
- The parallelism of lines in a plane is preserved by a translation in the plane.