symmetry n
1. (mathematics) an attribute of a shape or relation; exact correspondence of form on opposite sides of a dividing line or plane [syn: symmetricalness, correspondence, balance] [ant: asymmetry]
2. balance among the parts of something [syn: proportion] [ant: disproportion]
3. (physics) the property of being isotropic; having the same value when measured in different directions [syn: isotropy] [ant: anisotropy]

Symmetry \Sym"me*try\, n. [L. symmetria, Gr. ?; sy`n with, together + ? a measure: cf. F. sym['e]trie. See Syn-, and Meter rhythm.]
1. A due proportion of the several parts of a body to each other; adaptation of the form or dimensions of the several parts of a thing to each other; the union and conformity of the members of a work to the whole.
2. (Biol.) The law of likeness; similarity of structure; regularity in form and arrangement; orderly and similar distribution of parts, such that an animal may be divided into parts which are structurally symmetrical. Note: Bilateral symmetry, or two-sidedness, in vertebrates, etc., is that in which the body can be divided into symmetrical halves by a vertical plane passing through the middle; radial symmetry, as in echinoderms, is that in which the individual parts are arranged symmetrically around a central axis; serial symmetry, or zonal symmetry, as in earthworms, is that in which the segments or metameres of the body are disposed in a zonal manner one after the other in a longitudinal axis. This last is sometimes called metamerism.
3. (Bot.) (a) Equality in the number of parts of the successive circles in a flower. (b) Likeness in the form and size of floral organs of the same kind; regularity. Axis of symmetry. (Geom.) See under Axis. Respective symmetry, that disposition of parts in which only the opposite sides are equal to each other.

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Symmetry (from the Greek: "συμμετρεῖν" = to 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:

This article describes these notions of symmetry from four perspectives. The first is that of symmetry in geometry, which is the most familiar type of symmetry for many people. The second perspective is the more general meaning of symmetry in mathematics as a whole. The third perspective describes symmetry as it relates to science and technology. In this context, symmetries underlie some of the most profound results found in modern physics, including aspects of space and time. Finally, a fourth perspective discusses symmetry in the humanities, covering its rich and varied use in history, architecture, art, and religion.

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