Symmetry

OLS

Symmetry An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as Rotation, Reflection, Inversion, or more abstract operations). The mathematical study of symmetry is systematized and formalized in the extremely powerful and beautiful area of mathematics called Group Theory.
Symmetry can be present in the form of coefficients of equations as well as in the physical arrangement of objects. By classifying the symmetry of polynomial equations using the machinery of Group Theory, for example, it is possible to prove the unsolvability of the general Quintic Equation.
% [0 e' @; h- I0 |: A+ KIn physics, an extremely powerful theorem of Noether states that each symmetry of a system leads to a physically conserved quantity. Symmetry under Translation corresponds to momentum file:///E:/2009%201%2023/MCM/MCM/数学百科全书原版光盘ISO镜像/数学百科全书/Mathworld/images/physics.gif conservation, symmetry under Rotation to angular momentum file:///E:/2009%201%2023/MCM/MCM/数学百科全书原版光盘ISO镜像/数学百科全书/Mathworld/images/physics.gif conservation, symmetry in time to energy file:///E:/2009%201%2023/MCM/MCM/数学百科全书原版光盘ISO镜像/数学百科全书/Mathworld/images/physics.gif conservation, etc.