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What (who) is Symmetrical - definition
![Symmetry (left) and [[asymmetry]] (right)](https://commons.wikimedia.org/wiki/Special:FilePath/Asymmetric (PSF).svg?width=200 "Symmetry (left) and [[asymmetry]] (right)")
![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]].](https://commons.wikimedia.org/wiki/Special:FilePath/BigPlatoBig.png?width=200 "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]].")
![Great Mosque of Kairouan]] also called the Mosque of Uqba, in [[Tunisia]].](https://commons.wikimedia.org/wiki/Special:FilePath/Great Mosque of Kairouan, west portico of the courtyard.jpg?width=200 "Great Mosque of Kairouan]] also called the Mosque of Uqba, in [[Tunisia]].")
![The ceiling of [[Lotfollah mosque]], [[Isfahan]], [[Iran]] has 8-fold symmetries.](https://commons.wikimedia.org/wiki/Special:FilePath/Isfahan Lotfollah mosque ceiling symmetric.jpg?width=200 "The ceiling of [[Lotfollah mosque]], [[Isfahan]], [[Iran]] has 8-fold symmetries.")
![Clay pots thrown on a [[pottery wheel]] acquire rotational symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/Makingpottery.jpg?width=200 "Clay pots thrown on a [[pottery wheel]] acquire rotational symmetry.")
![A spherical [[symmetry group]] with [[octahedral symmetry]]. The yellow region shows the [[fundamental domain]].](https://commons.wikimedia.org/wiki/Special:FilePath/Sphere symmetry group o.svg?width=200 "A spherical [[symmetry group]] with [[octahedral symmetry]]. The yellow region shows the [[fundamental domain]].")
![[[Leonardo da Vinci]]'s '[[Vitruvian Man]]' (ca. 1487) is often used as a representation of symmetry in the human body and, by extension, the natural universe.](https://commons.wikimedia.org/wiki/Special:FilePath/Studio del Corpo Umano - Leonardo da Vinci.png?width=200 "[[Leonardo da Vinci]]'s '[[Vitruvian Man]]' (ca. 1487) is often used as a representation of symmetry in the human body and, by extension, the natural universe.")
![Seen from the side, the [[Taj Mahal]] has bilateral symmetry; from the top (in plan), it has fourfold symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/Taj Mahal, Agra views from around (85).JPG?width=200 "Seen from the side, the [[Taj Mahal]] has bilateral symmetry; from the top (in plan), it has fourfold symmetry.")
![The [[triskelion]] has 3-fold rotational symmetry.](https://commons.wikimedia.org/wiki/Special:FilePath/The armoured triskelion on the flag of the Isle of Man.svg?width=200 "The [[triskelion]] has 3-fold rotational symmetry.")
![p4 symmetry]]](https://commons.wikimedia.org/wiki/Special:FilePath/Zoomorphs.svg?width=200 "p4 symmetry]]")
Wikipedia
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Symmetry (from Ancient Greek: συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" 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 spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and 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 or a violation of symmetry.
