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, a symmetry is a movement of the figure so that it looks exactly the same after it has been moved.
Linguistic Note
The word symmetry comes from Greek συμμετρεῖν (symmetría) meaning measure together.
Sources
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 2$: Example $2.5$
- Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 26 \eta$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 34 \ (5)$
