Definition:Symmetry Mapping

Definition

A symmetry mapping 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 mapping is a movement of the figure so that it looks exactly the same after it has been moved.

Also known as

A symmetry mapping is often referred to just as a symmetry.

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

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Example $2.5$
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Definition of Group Structure: $\S 26 \eta$
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 34$. Examples of groups: $(5)$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): symmetry (of a geometric figure)