Symmetry (from 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, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so in this article they are discussed together.
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, theoretic models, language, music and even knowledge itself.
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.