Editing Symmetry (section)

{{Short description|Mathematical invariance under transformations}}
{{About|the broad concept}}
[[File:Asymmetric (PSF).svg|thumb|upright=1.25|Symmetry (left) and [[asymmetry]] (right)]]
[[File:Sphere symmetry group o.svg|thumb|upright=0.8|A spherical [[symmetry group]] with [[octahedral symmetry]]. The yellow region shows the [[fundamental domain]].]]
[[File:BigPlatoBig.png|thumb|upright=0.8|A [[fractal]]-like shape that has [[reflectional symmetry]], [[rotational symmetry]] and [[self-similarity]], three forms of symmetry. This shape is obtained by a [[finite subdivision rule]].]]
{{General geometry}}

'''Symmetry''' ({{etymology|grc|''{{Wikt-lang|grc|συμμετρία}}'' ({{grc-transl|συμμετρία}})|agreement in dimensions, due proportion, arrangement}})<ref>{{OEtymD|symmetry}}</ref> in everyday life refers to a sense of harmonious and beautiful proportion and balance.<ref>{{cite book |last=Zee|first=A. |title=Fearful Symmetry |publisher=[[Princeton University Press]] |location=[[Princeton, New Jersey]] |year=2007 |isbn=978-0-691-13482-6}}</ref><ref>{{cite book |title=Symmetry and the Beautiful Universe |last1=Hill|first1=C. T. |author1-link=Christopher T. Hill |last2=Lederman|first2=L. M. |author2-link=Leon M. Lederman |publisher=[[Prometheus Books]] |year=2005}}</ref>{{efn|For example, [[Aristotle]] ascribed spherical shape to the heavenly bodies, attributing this formally defined geometric measure of symmetry to the natural order and perfection of the cosmos.}} In [[mathematics]], the term has a more precise definition and is usually used to refer to an object that is [[Invariant (mathematics)|invariant]] under some [[Transformation (function)|transformations]], such as [[Translation (geometry)|translation]], [[Reflection (mathematics)|reflection]], [[Rotation (mathematics)|rotation]], or [[Scaling (geometry)|scaling]]. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.

Mathematical symmetry may be observed with respect to the passage of [[time]]; as a [[space|spatial relationship]]; through [[geometric transformation]]s; through other kinds of functional transformations; and as an aspect of [[abstract object]]s, including [[scientific model|theoretic models]], [[language]], and [[music]].<ref name="Mainzer000">{{cite book |title=Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science |first=Klaus|last=Mainzer |publisher=[[World Scientific]] |year=2005 |isbn=981-256-192-7}}</ref>{{efn|Symmetric objects can be material, such as a person, [[crystal]], [[quilt]], [[pamment|floor tiles]], or [[molecule]], or it can be an [[abstract object|abstract]] structure such as a [[mathematical equation]] or a series of tones (music).}}

This article describes symmetry from three perspectives: in [[mathematics]], including [[geometry]], the most familiar type of symmetry for many people; in [[science]] and [[nature]]; and in the arts, covering [[architecture]], [[art]], and music.

The opposite of symmetry is [[asymmetry]], which refers to the absence of symmetry.