Full back tattoo showing some taste of math. Symmetry 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.
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