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symmetry (n.)

1560s, "relation of parts, proportion," from French symmétrie (16c.) and directly from Latin symmetria, from Greek symmetria "agreement in dimensions, due proportion, arrangement," from symmetros "having a common measure, even, proportionate," from assimilated form of syn- "together" (see syn-) + metron "measure" (from PIE root *me- (2) "to measure"). Meaning "harmonic arrangement of parts" first recorded 1590s.

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Definitions of symmetry from WordNet

symmetry (n.)
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane;
Synonyms: symmetricalness / correspondence / balance
symmetry (n.)
balance among the parts of something;
Synonyms: proportion
symmetry (n.)
(physics) the property of being isotropic; having the same value when measured in different directions;
Synonyms: isotropy
From wordnet.princeton.edu