Symmetry

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 a transformation, such as reflection but including other transforms too.

Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.

The opposite of symmetry is asymmetry.

Perspectives

This article describes symmetry from three perspectives:

• In mathematics, including geometry
• In science and nature
• In the arts, covering architecture, art and music

Mathematics

Mathematical symmetry may be observed:

• With respect to the passage of time
• As a spatial relationship
• Through geometric transformations such as:
  • Scaling
  • Reflection
  • Rotation
• Through other kinds of functional transformations
• As abstract objects, theoretic models, language, music and even knowledge itself

See also

• Asymmetry
• Burnside's lemma
• Chirality
• Even and odd functions
• Fixed points of isometry groups in Euclidean space – center of symmetry
• Spacetime symmetries
• Spontaneous symmetry breaking
• Symmetry-breaking constraints
• Symmetric relation
• Symmetries of polyiamonds
• Symmetries of polyominoes
• Symmetry group
• Time symmetry
• Wallpaper group

External links

• Symmetry