Symmetry (from Greek συμμετρεῖν symmetría "measure together") generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection.
The second meaning is a precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system: by geometry, through physics or otherwise.
Although the meanings are distinguishable in some contexts, both meanings of "symmetry" are related and discussed in parallel.
The precise notions of symmetry have various measures and operational definitions. For example, symmetry may be observed
- with respect to the passage of time;
- as a spatial relationship;
- through geometric transformations such as scaling, reflection, and rotation;
- through other kinds of functional transformations; and
- as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.
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