Symmetry

Symmetry is invariance under specified transformations, such as rotations, reflections, or translations. The transformations that preserve an object or system form its symmetry group.

Transformation: A mapping that changes an object or its representation according to a rule. Symmetry is defined by which transformations leave a structure unchanged.
Rotational symmetry: Invariance of an object under rotation about an axis or around a point. It describes the repeated appearance of a structure after turning it by certain angles.
Noether's theorem: A theorem linking each continuous symmetry of a physical action to a conserved quantity. It turns continuous symmetries of physical laws into conservation laws such as energy and momentum.
Asymmetry: The absence of symmetry with respect to a specified transformation or comparison. It names the failure of a structure to remain unchanged under the chosen operations.
Bilateral symmetry: Symmetry in which a single plane divides an object into mirror-image halves. This body plan is widespread in animals and strongly shapes visual impressions of balance.
Invariance: The property of remaining unchanged under a specified transformation or change of representation. It is the defining test for whether a transformation is a symmetry.
Reflection symmetry: Invariance under reflection across a line, plane, or higher-dimensional mirror set. A mirror operation is one of the simplest ways a structure can remain unchanged.
Conservation law: A rule stating that a measurable quantity remains constant during specified physical processes. Symmetries explain why key quantities remain conserved as systems evolve.
Near-symmetry: Approximate invariance in which transformations preserve a structure only within some tolerance. Real objects often resemble ideal symmetric forms without satisfying exact invariance.
Radial symmetry: Symmetry around a central axis, with similar parts arranged around a center. It organizes flowers and many marine animals around a shared center.

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