Symmetry

Symmetry in mathematics

Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This can occur in many ways; for example, if X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups. If the object X is a set of points in the plane with its metric structure or any other metric space, a symmetry is a bijection of the set to itself which preserves the distance between each pair of points (i.e., an isometry). In general, every kind of structure in mathematics will have its own kind of symmetry, many of which are listed in the given points mentioned above. (Wikipedia).

Symmetry in mathematics
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▶ Topics ◀ Global / Local Symmetries, Continuous / Discrete Symmetries ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on

From playlist Symmetry

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From playlist New TED-Ed Originals

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This video was produced by Nina Qiu of Year 10 (2015).

From playlist Random

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From playlist Pre-Calculus

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From playlist Science Shorts and Explainers

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From playlist Feynman's Lectures

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From playlist MATH 1314: College Algebra (depreciated)

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From playlist Mysteries of Math and the Langlands Program (4 episodes broadcast on the Japanese TV channel NHK)

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From playlist Latest talks and lectures

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From playlist WSU Master Classes

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Differential equation | Congruence (geometry) | Translational symmetry | Vector space | Origin (mathematics) | Map (mathematics) | Permutation group | Symmetric group | Rational number | Periodic function | Elementary arithmetic | General linear group | Maclaurin series | Field extension | Square matrix | Real number | Isometry | Algebraic equation | Subgroup | Complex number | Kernel (algebra) | Reflection (mathematics) | Abelian group | Metric space | Symmetry | Hermitian matrix | Fourier series | Graded vector space | Permutation | Group isomorphism | Elementary symmetric polynomial | Rotational symmetry | Rigid body | Monic polynomial | Integer | Reflection symmetry | Complex conjugate | Symmetric algebra | Geometry | Antisymmetric relation | Symmetry (geometry) | Inner automorphism | Mathematical object | Set theory | Linear algebra | Self-adjoint operator | Invariant (mathematics) | Distance | Homogeneous polynomial | Polynomial | Factorial | Conjugate transpose | Degree (angle) | Mathematics | Bijection | System of differential equations | Euclidean group | Transpose | Function composition | Galois extension | Inner product space | Center (group theory) | Image (mathematics) | Order (group theory) | Absolute value | Operation (mathematics) | Finite set | Main diagonal | Group (mathematics) | Isomorphism | Antisymmetric tensor | Trivial group | Diagonal matrix | Error function | Multiple integral | Symmetry group | Field (mathematics) | Ring homomorphism | Ring (mathematics) | Tensor | Galois group | Integral | Abstract algebra | Graph of a function | Reduction of order | Skew-symmetric matrix