This article is about the broad concept. For other uses, see Symmetry (disambiguation).
Symmetry (left) and asymmetry (right)A spherical symmetry group with octahedral symmetry. The yellow region shows the fundamental domain.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.
Geometry
Projecting a sphere to a plane
Outline
History (Timeline)
Branches
Euclidean
Non-Euclidean
Elliptic
Spherical
Hyperbolic
Non-Archimedean geometry
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Discrete differential
Complex
Finite
Discrete/Combinatorial
Digital
Convex
Computational
Fractal
Incidence
Noncommutative geometry
Noncommutative algebraic geometry
Concepts
Features
Dimension
Straightedge and compass constructions
Angle
Curve
Diagonal
Orthogonality (Perpendicular)
Parallel
Vertex
Congruence
Similarity
Symmetry
Zero-dimensional
Point
One-dimensional
Line
segment
ray
Length
Two-dimensional
Plane
Area
Polygon
Triangle
Altitude
Hypotenuse
Pythagorean theorem
Parallelogram
Square
Rectangle
Rhombus
Rhomboid
Quadrilateral
Trapezoid
Kite
Circle
Diameter
Circumference
Area
Three-dimensional
Volume
Cube
cuboid
Cylinder
Dodecahedron
Icosahedron
Octahedron
Pyramid
Platonic Solid
Sphere
Tetrahedron
Four- / other-dimensional
Tesseract
Hypersphere
Geometers
by name
Aida
Aryabhata
Ahmes
Alhazen
Apollonius
Archimedes
Atiyah
Baudhayana
Bolyai
Brahmagupta
Cartan
Coxeter
Descartes
Euclid
Euler
Gauss
Gromov
Hilbert
Huygens
Jyeṣṭhadeva
Kātyāyana
Khayyám
Klein
Lobachevsky
Manava
Minkowski
Minggatu
Pascal
Pythagoras
Parameshvara
Poincaré
Riemann
Sakabe
Sijzi
al-Tusi
Veblen
Virasena
Yang Hui
al-Yasamin
Zhang
List of geometers
by period
BCE
Ahmes
Baudhayana
Manava
Pythagoras
Euclid
Archimedes
Apollonius
1–1400s
Zhang
Kātyāyana
Aryabhata
Brahmagupta
Virasena
Alhazen
Sijzi
Khayyám
al-Yasamin
al-Tusi
Yang Hui
Parameshvara
1400s–1700s
Jyeṣṭhadeva
Descartes
Pascal
Huygens
Minggatu
Euler
Sakabe
Aida
1700s–1900s
Gauss
Lobachevsky
Bolyai
Riemann
Klein
Poincaré
Hilbert
Minkowski
Cartan
Veblen
Coxeter
Present day
Atiyah
Gromov
v
t
e
Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement')[1] in everyday life refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] 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.
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, including theoretic models, language, and music.[4][b]
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, which refers to the absence of symmetry.
^Zee, A. (2007). Fearful Symmetry. Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-13482-6.
^Hill, C. T.; Lederman, L. M. (2005). Symmetry and the Beautiful Universe. Prometheus Books.
^Mainzer, Klaus (2005). Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science. World Scientific. ISBN 981-256-192-7.
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Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') in everyday life refers to a sense of harmonious...
Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen...
Facial symmetry is one specific measure of bodily symmetry. Along with traits such as averageness and youthfulness, it influences judgments of aesthetic...
molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a...
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn...
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an...
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure...
In physics, symmetry breaking is a phenomenon where a disordered but symmetric state collapses into an ordered, but less symmetric state. This collapse...
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. For example, a baseball...
fearful symmetry?). It has been used as the name of a number of other works: "Fearful Symmetry" (The X-Files), an episode of The X-Files "Fearful Symmetry",...
A plane symmetry is a symmetry of a pattern in the Euclidean plane: that is, a transformation of the plane that carries any direction lines to lines and...
global symmetry. Local symmetry, the cornerstone of gauge theories, is a stronger constraint. In fact, a global symmetry is just a local symmetry whose...
Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C)...
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group...
Origin of Symmetry is the second studio album by the English rock band Muse, released on 18 June 2001 through Taste Media. It was produced by John Leckie...
Time symmetry may refer to: Time translation symmetry Time reversal symmetry This disambiguation page lists articles associated with the title Time symmetry...
circular symmetry has all cyclic symmetry, Zn as subgroup symmetries. Reflective circular symmetry has all dihedral symmetry, Dihn as subgroup symmetries. In...
hexagon has six rotational symmetries (rotational symmetry of order six) and six reflection symmetries (six lines of symmetry), making up the dihedral group...
translational symmetry is the invariance of a system of equations under any translation (without rotation). Discrete translational symmetry is invariant...
implying no symmetry. On the regular octagon, there are eleven distinct symmetries. John Conway labels full symmetry as r16. The dihedral symmetries are divided...
the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive translation...
crystallography, a symmetry element is a point, line, or plane about which symmetry operations can take place. In particular, a symmetry element can be a...
the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory...
Floral symmetry describes whether, and how, a flower, in particular its perianth, can be divided into two or more identical or mirror-image parts. Uncommonly...
four lines of reflectional symmetry and it has rotational symmetry of order 4 (through 90°, 180° and 270°). Its symmetry group is the dihedral group D4...
ground state, the continuous translational symmetry in space is broken and replaced by the lower discrete symmetry of the periodic crystal. As the laws of...
The symmetry number or symmetry order of an object is the number of different but indistinguishable (or equivalent) arrangements (or views) of the object...
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