symmetry

Also known as lack of asymmetry

thumb|upright=1.25|Symmetry (left) and asymmetry (right) thumb|upright=0.8|A spherical symmetry group with [[octahedral symmetry. The yellow region shows the fundamental domain.]] thumb|upright=0.8|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.]]

AI overview

Symmetry is a property where an object or pattern looks the same after certain transformations, such as being reflected, rotated, or subdivided in particular ways. It matters because it appears throughout nature and mathematics, helping scientists and mathematicians understand the structure and behavior of everything from crystals to fractals to fundamental forces.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

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hashtag: Symmetry
Commons category: Symmetry
Commons gallery: Symmetry

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27 sections

Contents

In mathematics
In geometry
In logic
Other areas of mathematics
In science and nature
In physics
In biology
In chemistry
In psychology and neuroscience
In social interactions
In the arts
In architecture
In pottery and metal vessels
In carpets and rugs
In quilts
In other arts and crafts
In music
Musical form
Pitch structures
Equivalency
In aesthetics
In literature
See also
Explanatory notes
References
Further reading
External links

Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.