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.
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.
The opposite of symmetry is asymmetry.
Other articles related to "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 ... cases where the parts can be divided into two sets, each giving a solid with as much symmetry as the whole figure ...
... 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 ...
... 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 ...
... 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 health ... that in turn drives a powerful tendency to create artifacts with similar symmetry ...
... 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 sides have the same color ...
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)