symmetry
Sign in to savethumb|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.
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27 sectionsContents
- 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
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.]]
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.