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 .
The opposite of symmetry is asymmetry.