# Symmetry

## Mathematical #invariance under transformations / From Wikipedia, the free encyclopedia

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**Symmetry** (from Ancient Greek: συμμετρία *symmetria* "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][lower-alpha 1] 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.

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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.[4][lower-alpha 2]

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.