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.
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Some articles on symmetry:
... reflects the fact that it is invariant under the action of a group symmetry, such as translational invariance ... Thus a symmetry in the Hamiltonian becomes a symmetry of the correlation function (and vice-versa) ... This symmetry has a critically important interpretation in probability theory it implies that the Gibbs measure has the Markov property that is, it is ...
... Symmetry suggests that the probability is independent of the color chosen, so that the information about which color is shown does not affect the odds that both ...
... The relationship of symmetry to aesthetics is complex ... Certain simple symmetries, and in particular bilateral symmetry, seem to be deeply ingrained in the inherent perception by humans of the likely ... tendency to create artifacts with similar symmetry ...
... (iii) The parts included in any one plane must have trigonal symmetry, without or with reflection ... This secures icosahedral symmetry for the whole solid ... where the parts can be divided into two sets, each giving a solid with as much symmetry as the whole figure ...
... In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects by finding the topological skeleton ... The medial axis, a subset of the symmetry set is a set of curves which roughly run along the middle of an object ...
More definitions of "symmetry":
- (noun): (mathematics) an attribute of a shape or relation; exact correspondence of form on opposite sides of a dividing line or plane.
Synonyms: symmetricalness, correspondence, balance
- (noun): (physics) the property of being isotropic; having the same value when measured in different directions.
Famous quotes containing the word symmetry:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (17881824)